1. Today
Make-Up Tests?
 Khan Academy Review
 Review for Friday’s Test
 New Material: Distance & Mid-Point
Formulas
Class Work
May 14

2. Warm-Up

3. Khan Academy: Radical Equations

4. Khan Academy: Pythagorean Theorem
81 – 26 = 𝟓𝟔
= 7.48
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?

5. Test Review: Radical Operations: (4)
The problems on Friday’s test aren’t necessarily more
difficult, there are just more types of problems to prepare
for. Today and tomorrow, we will review each type.

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

8. 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

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

10. 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....
=

11. 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 )

12. Find the distance between the two points
(3, 𝟒) (9, −𝟒)
(x1,y1) (x2, y2)
𝒅 = (𝒙 𝟐 − 𝒙 𝟏) 𝟐+(𝒚 𝟐 − 𝒚 𝟏) 𝟐
𝒅 = 𝟗 − (𝟑) 𝟐 + (−𝟒 − 𝟒) 𝟐
𝒅 = 𝟔 𝟐 + (−𝟖) 𝟐
𝒅 = 𝟏𝟎𝟎
𝒅 = 𝟏𝟎

13. Find the distance of the line.
1. (−𝟒, 1) (−𝟐, 3)(x1, y1) (x2, y2)
𝒅 = (𝒙 𝟐 − 𝒙 𝟏) 𝟐+(𝒚 𝟐 − 𝒚 𝟏) 𝟐
𝒅 = (−𝟐 − −𝟒 ) 𝟐+(𝟑 − 𝟏) 𝟐
𝒅 = 𝟐 𝟐 + (𝟐) 𝟐
𝒅 = 𝟐 𝟐
𝒅 = 𝟒 + 𝟒
𝒅 = 𝟖
𝒅 = 𝟐 ∙ 𝟒

14. Find the distance between:

15. The Distance Formula:

16. Class Work:
See Handout

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