The document provides information about topics covered in math class today including: - Reviewing for the final exam by practicing adding, subtracting, multiplying, and dividing fractions. - Using the Pythagorean theorem and distance formula to solve problems finding the distance between two points on a graph or with coordinates. - Examples are given for using the distance formula when all four coordinates are known or when three are known and the distance is solved for. - A review of graphing terminology like quadrants, the origin, and ordering of x and y coordinates.

1. Today
 Make-Up Tests?
 Review For Final Exam
 Review Pythagorean Theorem
New Material: Distance Formula
Class Work 4.10
May 13

2. 2
x2
– x + 2 = 0
(x – 2)(x + 1) Solutions are: x = 2, x = -1
Extraneous Solution is x = -1
Final Exam Review:
Add, Subtract, Multiply, & Divide
𝟑
𝟖
and
𝟕
𝟗
. Reduce to its simplest terms.
a.
𝟑
𝟖
+
𝟕
𝟗
=
𝟑
𝟖
+
𝟕
𝟗
=
𝟖𝟑
𝟕𝟐
= b.
𝟑
𝟖
-
𝟕
𝟗
=
𝟐𝟕−𝟓𝟔
𝟕𝟐
= -
𝟐𝟗
𝟕𝟐
c.
𝟑
𝟖
•
𝟕
𝟗
=
𝟐𝟏
𝟕𝟐
=
𝟕
𝟐𝟒
d.
𝟑
𝟖
÷
𝟕
𝟗
=
𝟑
𝟖
•
𝟗
𝟕
=
𝟐𝟕
𝟓𝟔
=
1
𝟏𝟏
𝟕𝟐

3. Pythagorean Theorem
81 – 26 = 𝟓𝟔 =
A building is on fire and
you need to set the
ladder back 10 ft. to
prevent burning. What is
the shortest ladder (in
feet) that will reach the
third story window ?
What is the
perimeter of
the sail?
9' + 12' + 15' = 36'
2 𝟏𝟒

5. The distance between A and B is
| | | | | | | | | | | | | |
-5 4
A B
| -5 – 4 | = | -9 | = 9
Remember: Distance is always positive

6. A
B
The Distance Formula Is Derived
From The Pythagorean Formula
6
15
6² + 15² = C²
𝟐𝟔𝟏=C
As you can see, the shortest distance between two points is...
A straight line; 16.16 < 21

7. Distance Formula
Dist. = ( x2 - x1 )² + ( y2 - y1 )²
Remember the order ( x , y )
All answers are positive

8. Find the distance between the two points on the graph.
The Distance Formula:
What is the distance
along the x axis?
What is the distance
along the y axis?
Let's first use the P.T. to find the distance: a2 + b2 = c2
Now, let's use the distance
formula....
52 + 42 = 412

9. Find the distance between:
( 3 – 8 )² + ( 6 - 10 )²
( -5 )² + ( -4 )²
25 + 16
41 = 6.40
( 8 – 3 )² + ( 10 – 6 )²
( 5 )² + ( 4 )²
25 + 16
41 =6.40
( 3, 6 ) and ( 8, 10 )
Find the distance between:
( 8, 10 ) and ( 3, 6 )
When Using the distance formula, it does not matter what
point is used for x1 and x2. Be sure your y1 is from the same
coordinate pair as the x1

10. Find the distance between the two points
(x1,y1) (x2, y2)

11. Find the distance of the line.
(x1, y1) (x2, y2)

12. Find the distance between:
12 − 6 + (3 5 2 5)
2 2
= 45 – 30 – 30 + 20

13. The Distance Formula
There are two different types of problems to solve withe
the distance formula.
A. All four of the coordinates are known. Solve for the
distance.
B. Three of four coordinates and the distance is known.
Solve for the fourth coordinate.

14. Example 1. Find the distance between the two points.
(-2,5) and (3,-1)
• Let (x1,y1) = (-2,5) and (x2,y2) = (3,-1)
A. All four of the coordinates are known. Solve for the distance.

15. Example 2.

16. B. Three of four coordinates and the distance is known.
Solve for the fourth coordinate.

17. B. Three of four coordinates and the distance is known.
Solve for the fourth coordinate.

18. Class Work: 4.10

19. Review Graphing
y
x
( 0,0 )
Origin
Positive
Negative
Order ( X,Y )
Quadrant
I
Quadrant
II
Quadrant
III
Quadrant
IV

20. Khan Academy: Radical Equations