The document discusses finding the midpoint of a line segment on a number line and on a coordinate plane. It defines the midpoint as the point that bisects the segment. It provides formulas for calculating the x- and y-coordinates of the midpoint given the endpoints' coordinates. Several examples are worked through, finding midpoints of segments with given endpoints on a coordinate plane using the midpoint formulas.
Find the midpoint of two given points.
Find the coordinates of an endpoint given one endpoint and a midpoint.
Find the coordinates of a point a fractional distance from one end of a segment.
Find the midpoint of two given points.
Find the coordinates of an endpoint given one endpoint and a midpoint.
Find the coordinates of a point a fractional distance from one end of a segment.
Find the midpoint of two given points.
Find the coordinates of an endpoint given one endpoint and a midpoint.
Find the coordinates of a point a fractional distance from one end of a segment.
Find the distance between two points
Find the midpoint between two points
Find the coordinates of a point a fractional distance from one end of a segment
* Find the distance between two points
* Find the midpoint of two given points
* Find the coordinates of an endpoint given one endpoint and a midpoint
* Find the coordinates of a point a fractional distance from one end of a segment
The student is able to (I can):
• Find the midpoint of two given points.
• Find the coordinates of an endpoint given one endpoint
and a midpoint.
• Find the distance between two points.
Math 2318 - Test 3In this test we will try something differe.docxandreecapon
Math 2318 - Test 3
In this test we will try something different. The answers are provided, your job is to show the work in how to get that
solution. On problem 1 only A is a vector space. You will show why it is a vector space but you will also show why B
and C are not vector spaces. On question 2 only V is a vector space. You will show why it is a vector space and you
will also show why W and U are not vector spaces.
Solve the problem.
1) Determine which of the following sets is a subspace of Pn for an appropriate value of n.
A: All polynomials of the form p(t) = a + bt2, where a and b are in ℛ
B: All polynomials of degree exactly 4, with real coefficients
C: All polynomials of degree at most 4, with positive coefficients
A) A and B B) C only C) A only D) B only
1)
2) Determine which of the following sets is a vector space.
V is the line y = x in the xy-plane: V = x
y
: y = x
W is the union of the first and second quadrants in the xy-plane: W = x
y
: y ≥ 0
U is the line y = x + 1 in the xy-plane: U = x
y
: y = x + 1
A) U only B) V only C) W only D) U and V
2)
Find a matrix A such that W = Col A.
3) W =
3r - t
4r - s + 3t
s + 3t
r - 5s + t
: r, s, t in ℛ
A)
0 3 -1
4 -1 3
0 1 3
1 -5 1
B)
3 0 -1
4 -1 3
0 1 3
1 -5 1
C)
3 -1
4 3
1 3
1 -5
D)
3 4 0 1
0 -1 1 -5
-1 3 3 1
3)
Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
4) u =
5
-3
5
, A =
1 -3 4
-1 0 -5
3 -3 6
A) In Col A and in Nul A B) In Col A, not in Nul A
C) Not in Col A, in Nul A D) Not in Col A, not in Nul A
4)
Use coordinate vectors to determine whether the given polynomials are linearly dependent in P2. Let B be the standard
basis of the space P2 of polynomials, that is, let B = 1, t, t2 .
5) 1 + 2t, 3 + 6t2, 1 + 3t + 4t2
A) Linearly dependent B) Linearly independent
5)
Find the dimensions of the null space and the column space of the given matrix.
6) A = 1 -5 -4 3 0
-2 3 -1 -4 1
A) dim Nul A = 2, dim Col A = 3 B) dim Nul A = 4, dim Col A = 1
C) dim Nul A = 3, dim Col A = 2 D) dim Nul A = 3, dim Col A = 3
6)
1
Solve the problem.
7) Let H =
a + 3b + 4d
c + d
-3a - 9b + 4c - 8d
-c - d
: a, b, c, d in ℛ
Find the dimension of the subspace H.
A) dim H = 3 B) dim H = 1 C) dim H = 4 D) dim H = 2
7)
Assume that the matrix A is row equivalent to B. Find a basis for the row space of the matrix A.
8) A =
1 3 -4 0 1
2 4 -5 5 -2
1 -5 0 -3 2
-3 -1 8 3 -4
, B =
1 3 -4 0 1
0 -2 3 5 -4
0 0 -8 -23 17
0 0 0 0 0
A) {(1, 3, -4, 0, 1), (0, -2, 3, 5, -4), (0, 0, -8, -23, 17), (0, 0, 0, 0, 0)}
B) {(1, 3, -4, 0, 1), (0, -2, 3, 5, -4), (0, 0, -8, -23, 17)}
C) {(1, 3, -4, 0, 1), (2, 4, -5, 5), -2, (1, ...
Students learn the definition of slope and calculate the slope of lines.
Students also learn to consider the slopes of parallel lines and perpendicular lines.
Students learn to define and identify linear equations. They also learn the definition of Standard Form of a linear equation.
Students also learn to graph linear equations using x and y intercepts.
[Note: This is a partial preview. To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
Sustainability has become an increasingly critical topic as the world recognizes the need to protect our planet and its resources for future generations. Sustainability means meeting our current needs without compromising the ability of future generations to meet theirs. It involves long-term planning and consideration of the consequences of our actions. The goal is to create strategies that ensure the long-term viability of People, Planet, and Profit.
Leading companies such as Nike, Toyota, and Siemens are prioritizing sustainable innovation in their business models, setting an example for others to follow. In this Sustainability training presentation, you will learn key concepts, principles, and practices of sustainability applicable across industries. This training aims to create awareness and educate employees, senior executives, consultants, and other key stakeholders, including investors, policymakers, and supply chain partners, on the importance and implementation of sustainability.
LEARNING OBJECTIVES
1. Develop a comprehensive understanding of the fundamental principles and concepts that form the foundation of sustainability within corporate environments.
2. Explore the sustainability implementation model, focusing on effective measures and reporting strategies to track and communicate sustainability efforts.
3. Identify and define best practices and critical success factors essential for achieving sustainability goals within organizations.
CONTENTS
1. Introduction and Key Concepts of Sustainability
2. Principles and Practices of Sustainability
3. Measures and Reporting in Sustainability
4. Sustainability Implementation & Best Practices
To download the complete presentation, visit: https://www.oeconsulting.com.sg/training-presentations
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The world of search engine optimization (SEO) is buzzing with discussions after Google confirmed that around 2,500 leaked internal documents related to its Search feature are indeed authentic. The revelation has sparked significant concerns within the SEO community. The leaked documents were initially reported by SEO experts Rand Fishkin and Mike King, igniting widespread analysis and discourse. For More Info:- https://news.arihantwebtech.com/search-disrupted-googles-leaked-documents-rock-the-seo-world/
Cracking the Workplace Discipline Code Main.pptxWorkforce Group
Cultivating and maintaining discipline within teams is a critical differentiator for successful organisations.
Forward-thinking leaders and business managers understand the impact that discipline has on organisational success. A disciplined workforce operates with clarity, focus, and a shared understanding of expectations, ultimately driving better results, optimising productivity, and facilitating seamless collaboration.
Although discipline is not a one-size-fits-all approach, it can help create a work environment that encourages personal growth and accountability rather than solely relying on punitive measures.
In this deck, you will learn the significance of workplace discipline for organisational success. You’ll also learn
• Four (4) workplace discipline methods you should consider
• The best and most practical approach to implementing workplace discipline.
• Three (3) key tips to maintain a disciplined workplace.
Enterprise Excellence is Inclusive Excellence.pdfKaiNexus
Enterprise excellence and inclusive excellence are closely linked, and real-world challenges have shown that both are essential to the success of any organization. To achieve enterprise excellence, organizations must focus on improving their operations and processes while creating an inclusive environment that engages everyone. In this interactive session, the facilitator will highlight commonly established business practices and how they limit our ability to engage everyone every day. More importantly, though, participants will likely gain increased awareness of what we can do differently to maximize enterprise excellence through deliberate inclusion.
What is Enterprise Excellence?
Enterprise Excellence is a holistic approach that's aimed at achieving world-class performance across all aspects of the organization.
What might I learn?
A way to engage all in creating Inclusive Excellence. Lessons from the US military and their parallels to the story of Harry Potter. How belt systems and CI teams can destroy inclusive practices. How leadership language invites people to the party. There are three things leaders can do to engage everyone every day: maximizing psychological safety to create environments where folks learn, contribute, and challenge the status quo.
Who might benefit? Anyone and everyone leading folks from the shop floor to top floor.
Dr. William Harvey is a seasoned Operations Leader with extensive experience in chemical processing, manufacturing, and operations management. At Michelman, he currently oversees multiple sites, leading teams in strategic planning and coaching/practicing continuous improvement. William is set to start his eighth year of teaching at the University of Cincinnati where he teaches marketing, finance, and management. William holds various certifications in change management, quality, leadership, operational excellence, team building, and DiSC, among others.
Personal Brand Statement:
As an Army veteran dedicated to lifelong learning, I bring a disciplined, strategic mindset to my pursuits. I am constantly expanding my knowledge to innovate and lead effectively. My journey is driven by a commitment to excellence, and to make a meaningful impact in the world.
Affordable Stationery Printing Services in Jaipur | Navpack n PrintNavpack & Print
Looking for professional printing services in Jaipur? Navpack n Print offers high-quality and affordable stationery printing for all your business needs. Stand out with custom stationery designs and fast turnaround times. Contact us today for a quote!
Accpac to QuickBooks Conversion Navigating the Transition with Online Account...PaulBryant58
This article provides a comprehensive guide on how to
effectively manage the convert Accpac to QuickBooks , with a particular focus on utilizing online accounting services to streamline the process.
What are the main advantages of using HR recruiter services.pdfHumanResourceDimensi1
HR recruiter services offer top talents to companies according to their specific needs. They handle all recruitment tasks from job posting to onboarding and help companies concentrate on their business growth. With their expertise and years of experience, they streamline the hiring process and save time and resources for the company.
What are the main advantages of using HR recruiter services.pdf
Midpoints (Geometry 2_5)
1. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn B A C
2. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn The midpoint of a line segment, , is the point C that ______ the segment. B A C
3. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects The midpoint of a line segment, , is the point C that ______ the segment. B A C
4. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C
5. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects C = [3 + (-5)] ÷ 2 The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C
6. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects C = [3 + (-5)] ÷ 2 = (-2) ÷ 2 The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C
7. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects C = [3 + (-5)] ÷ 2 = (-2) ÷ 2 = -1 The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C
8. Midpoints On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is Theorem 2 – 5
9. Midpoints On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is Theorem 2 – 5
10. Midpoints On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is Theorem 2 – 5 A B
11. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 A B
12. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 A B
13. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 x A B
14. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 Consider the y-coordinate: It will be ( midway ) between the lines y = 3 and y = 7 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 x A B
15. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 Consider the y-coordinate: It will be ( midway ) between the lines y = 3 and y = 7 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 x y A B
16. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 Consider the y-coordinate: It will be ( midway ) between the lines y = 3 and y = 7 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A B x y C(x, y)
17. Midpoints On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6
18. Midpoints On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6
19. Midpoints O y x On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6
20. Midpoints O y x On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6
21. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 A(1, 7) B(9, 3)
22. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 x A(1, 7) B(9, 3)
23. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 x y A(1, 7) B(9, 3)
24. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A(1, 7) B(9, 3) x y
25. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A(1, 7) B(9, 3) x y
26. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A(1, 7) B(9, 3) x y C(5, 5)
27. Midpoints Graph A(1, 1) and B(7, 9) 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.
28. Midpoints Graph A(1, 1) and B(7, 9) Check your answer using the midpoint formula. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.
29. Midpoints Graph A(1, 1) and B(7, 9) Check your answer using the midpoint formula. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.
30. Midpoints Graph A(1, 1) and B(7, 9) C Check your answer using the midpoint formula. C(4, 5) 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.
31. Midpoints 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)
32. Midpoints B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)
33. Midpoints x-coordinate of B y-coordinate of B B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)
34. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)
35. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 Multiply each side by 2 B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)
36. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 Multiply each side by 2 Add or subtract to isolate the variable B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)
37. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 Multiply each side by 2 Add or subtract to isolate the variable B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) B(-1, 8) C(3, 5)