The document contains two worksheets that ask students to calculate the coordinates of the midpoint of lines joining pairs of points. Worksheet 1 contains problems with points in 2D and 3D space. Worksheet 2 contains additional problems finding midpoints of lines between points in 2D and 3D space. The worksheets provide practice calculating midpoints using coordinate geometry.
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.
1.Determine whether the relation is a function.{(-.docxfredellsberry
1.
Determine whether the relation is a function.
{(-2, -7), (3, -5), (6, -4), (9, -6), (10, -1)}
A) Not a function
B) Function
2.
Determine whether the relation is a function.
{(-5, -4), (-2, 9), (-1, -2), (-1, 7)}
A) Function
B) Not a function
3.
Determine whether the relation is a function.
{(-7, -1), (-7, 2), (-1, 8), (3, 3), (10, -7)}
A) Not a function
B) Function
4.
Determine whether the relation is a function.
{(1, -3), (1, 1), (6, -8), (9, -3), (11, -3)}
A) Not a function
B) Function
5.
Determine whether the relation is a function.
{(-6, -9), (-2, 1), (1, -1), (7, -7)}
A) Not a function
B) Function
6.
Determine whether the equation defines y as a function of x.
x + y = 9
A) y is a function of x
B) y is not a function of x
7.
Determine whether the equation defines y as a function of x.
x2 + y2 = 1
A) y is a function of x
B) y is not a function of x
8.
Determine whether the equation defines y as a function of x.
x = y2
A) y is a function of x
B) y is not a function of x
9.
Evaluate the function at the given value of the independent variable and simplify.
f(x) = -3x - 8; f(-2)
A) 14
B) -11
C) -2
D) 22
10.
Evaluate the function at the given value of the independent variable and simplify.
f(x) = x2 - 1; f(x - 2)
A) x2 + 4
B) x2 - 4x + 3
C) x2 - 3
D) x2 - 4x + 4
11.
Evaluate the function at the given value of the independent variable and simplify.
f(x) = 4x2 + 5x - 6; f(x - 1)
A) -3x2 + 4x - 7
B) 4x2 - 3x - 7
C) 4x2 - 3x + 3
D) 4x2 - 19x + 3
12.
Evaluate the function at the given value of the independent variable and simplify.
f(x) = ; f(5)
A)
B)
C)
D)
13.
Find the slope of the line that goes through the given points.
(3, -5), (-9, -8)
A) -
B)
C)
D) 4
14.
Find the slope of the line that goes through the given points.
(-7, 6), (-7, -9)
A) Undefined
B)
C) 0
D) -
15.
Find the slope of the line that goes through the given points.
(-1, 4), (5, 4)
A)
B) 0
C) 2
D) Undefined
16.
Find the slope of the line that goes through the given points.
(-2, -6), (-9, -17)
A)
B)
C) -
D)
17.
Find the slope of the line that goes through the given points.
(-8, 8), (-5, 2)
A)
B)
C) -
D) - 2
18.
Find the slope of the line that goes through the given points.
(-3, -7), (9, -7)
A) 0
B) 1
C) -4
D) 4
19.
Use the given conditions to write an equation for the line in point-slope form.
Slope = 4, passing through (-3, 7)
A) y - 7 = 4(x + 3)
B) y = 4x + 19
C) x - 7 = 4(y + 3)
D) y + 7 = 4(x - 3)
20.
Use the given conditions to write an equation for the line in point-slope form.
Slope = , passing through (8, 7)
A) x - 7 = (y - 8)
B) y - 7 = (x - .
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.
Investigate how to find the gradient of a line given two coordinates
Starter questions on first slide of PowerPoint.
Go through the lesson objective and outcomes with the class then ask students to complete the worksheet plotting coordinates. Tell the class they have 2-3 minutes to do this. The task is to recap on plotting coordinates and iron out any misconceptions. Ask pupils to have a think about what is the same and what is different about these triangles. Ask which quadrant each triangle is in and if any lines are parallel or perpendicular. Ask pupils to show how many triangles they drew correctly by number of fingers.
10-15 mins - Go through slides 9-12 explaining gradient then pupils do the question shown on slide 13 (mini-whiteboards). Give out worksheets while pupils are doing this so they can move onto that when they finish question on the board. Pupils swap papers and mark. Ask for hands up who got one/two/three/four/five answers correct. Ask pupils what is the same and what is different about these lines emphasising negative/positive gradient. Extension worksheets prepared for anyone that finishes.
10-15 mins – Go through slides 16-17 then ask pupils to do the next two questions on laminated grid (whiteboard).
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1. Worksheet1
1. Work out the coordinates of the midpoint of the line joining:
a. (7,3) and (11,1) b. (8, -4) and (-2, 0)
c. (-3, 4) and (3, -4) d. (6, -2) and (-7, 1)
e. (0, -5) and (9, -11) f. (-9, -1) and (-3, -4)
2. Work out the coordinates of the midpoint of the line joining:
a. (2, 0, 4) and (0, 6, 0) b. (1, 4, 6) and (3, 2, 0)
c. (-4, 6, 1) and (3, -2, 2) d. (-1, -1, -1) and (3, 6, 2)
e. (4, 7, -3) and (-3, 11, -7) f. (-4, -2, -9) and (-4, -1, -12)
Worksheet1
1. Work out the coordinates of the midpoint of the line joining:
a. (7,3) and (11,1) b. (8, -4) and (-2, 0)
c. (-3, 4) and (3, -4) d. (6, -2) and (-7, 1)
e. (0, -5) and (9, -11) f. (-9, -1) and (-3, -4)
2. Work out the coordinates of the midpoint of the line joining:
a. (2, 0, 4) and (0, 6, 0) b. (1, 4, 6) and (3, 2, 0)
c. (-4, 6, 1) and (3, -2, 2) d. (-1, -1, -1) and (3, 6, 2)
e. (4, 7, -3) and (-3, 11, -7) f. (-4, -2, -9) and (-4, -1, -12)
Worksheet2
1. Work out the coordinates of the midpoint of the line joining:
a. (2, 5) and (12, 29) b. (-4, -6) and (6, 12)
c. (9, -15) and (-11, 6) d. (0, -5) and (-9, -11)
e. (-7, -8) and (-12, -4) f. (-6, -5) and (-5, -6)
2. Work out the coordinates of the midpoint of the line joining:
a. (-4, 6, 1) and (3, -2, 2) b. (-1, -1, -1) and (3, 6, 2)
c. (4, 7, -3) and (-3, 11, -7) d. (-4, -2, -9) and (-4, -1, -12)
e. (2, -5, 13) and (-22, 8, 7) f. (1.5, -6, 3.5) and (2, -11, -4.5)
Worksheet2
1. Work out the coordinates of the midpoint of the line joining:
a. (2, 5) and (12, 29) b. (-4, -6) and (6, 12)
c. (9, -15) and (-11, 6) d. (0, -5) and (-9, -11)
e. (-7, -8) and (-12, -4) f. (-6, -5) and (-5, -6)
2. Work out the coordinates of the midpoint of the line joining:
a. (-4, 6, 1) and (3, -2, 2) b. (-1, -1, -1) and (3, 6, 2)
c. (4, 7, -3) and (-3, 11, -7) d. (-4, -2, -9) and (-4, -1, -12)
e. (2, -5, 13) and (-22, 8, 7) f. (1.5, -6, 3.5) and (2, -11, -4.5)
