The document provides information about topics to be covered in class today including warm-ups, make-up tests, reviews of radical equations, Pythagorean theorem, distance and midpoint formulas, and STAR testing. It then reviews solving radical equations, using the Pythagorean theorem, and applying the distance and midpoint formulas to different types of problems. Examples are provided for using the distance and midpoint formulas to find missing coordinates given certain known values.

1. Today:
 Warm-Up
Make-Up Tests?
Alt.Khan Due Today
Review: Radical Equations, Pythagorean
Theorem, Distance & Midpoint Formulas
Class Work
STAR Testing
May 19

2. Radical Operations Review:
10 10S =

3. Last Radical Test Review:
= 214.86972 feet; = 215 feet
Pythagorean Theorem

4. Last Radical Test Review:
Radical Equations:
s = 60
24 + 8q = 9 + 6q + q2
0 = -15 + 2q + q2
q2
- 2q -15 = 0
(q - 5)(q + 3) = 0
q = 5, q = -3Check to see if one or both are
extraneous solutions
Both are
solutions

5. 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.

6. A. All four of the coordinates are known. Solve for the distance.

7. B. Three of four coordinates and the distance is known.
Solve for the fourth coordinate.
a2 – 6a – 16 = 0 (a – 8) (a + 2) = 0 a = 8, a = -2
Plug in to check

8. MIDPOINT
• The point halfway between the endpoints of a line
segment is called the midpoint. A midpoint divides
a line segment into two equal segments.
• Just as there are two different types of problems
involving the distance formula, there are two
different types of midpoint problems.
1. Both endpoints are given, and the midpoint must
be found.
2. One endpoint and the midpoint are given; the other
endpoint must be found.

9. To find the midpoint
of the line along the x
axis..
Add the |beginning
coordinate| and the
|ending coordinate|,
then ÷ 2
To find the midpoint
of the line along the y
axis, find the ‘average’
y value
The average y value of
the line segment is...
The mid-point is at
(0,5)
What are the x
coordinates of the end
points of the line
segment?
The average x value of
the line segment is...
What are the y
coordinates of the end
points of the line
segment?
The mid-point
coordinates are.. (1,0)
The mid-point
coordinates are...

10. • If the line segments are vertical or horizontal, you
may find the midpoint by simply dividing the
length of the segment by 2 and counting that
value from either of the endpoints.
= The Average

11. 6
10
Midpoint
If the line segments are diagonally positioned, more
thought must be paid to the solution. When you are
finding the coordinates of the midpoint of a segment,
you are actually finding the the x-coordinates and
the y-coordinates.

12. Midpoint Formula
X + X , Y + Y
2 2

13. Example 1:

14. X1 + X2
2
= XMID Y1 + Y2
2
= YMID
What If We Knew The Midpoint Of A
Segment And One Endpoint? How Would We
Find The Other Endpoint?
Think Of The Formula As:
Plug in the given
and solve for the
unknown
Given an endpoint ( 3,5 ), and midpoint
( 6, -2 ), find the other endpoint.

15. X1 + X2
2
= XMID Y1 + Y2
2
= YMID
Find ( X2 ,Y2 )
3 + X2 =
6
12
5 + Y2 =
-2
-4
(9, -9)
3 + X2 =
2
X2 = 9
5 + Y2 =
2
Y2 = -9
( X2 ,Y2 ) =

16. Example 2:
M is the mid-point. The coordinates M (-1,1) and C
(1,-3) are given. Find the coordinates of point D.
Find ( X2 ,Y2 ) X1 + X2
2
= XMID Y1 + Y2
2
= YMID
M
C
D = (-3,5)

17. A variation of the second type of midpoint problem.
Find the missing value of h in the points (5,7) and
(1,h) if its midpoint lies at (3, -2)