The document provides information about reviewing radical operations, distance and midpoint formulas, and examples of using these formulas to solve problems. It includes: - Examples of using the distance formula to find the distance between two points when all coordinates are known, and using three coordinates and the distance to find the unknown coordinate. - The definition of a midpoint as the point halfway between the x-coordinates and y-coordinates of two endpoints. - The midpoint formula for finding the x-coordinate and y-coordinate of the midpoint using the endpoints' coordinates. - An example of using a known midpoint and one endpoint to find the other unknown endpoint.

1. Today:
Review Radical Operations
Distance & Mid-Point Formulas
Class Work
May 15

2. Test Review(6)
Find the area of the triangle:
The square root of the product of two positive numbers
equals 6. One number is nine less than the other number.
What are the numbers?
The numbers are:
x = 12, x = 3

3. Test Review (6)
15
1560 
= 5

4. For high school wrestling
competitions, the wrestling
mat must be a square with
an area of 625 square feet.
What is the length of each
side of the mat?
25 feet
Square Root Applications:
x2
+ 3x2
= 𝟒𝟎
2

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. 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.

7. Example 2.

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

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

10. MIDPOINT
The midpoint of a segment is half way
between the x’s and half way between the y’s
You can call it the average
6
10
Midpoint

11. 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...

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

13. 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:
Midpoint
( Xmid , Ymid )( X1 , Y1 ) ( X2 , Y2 )
Endpoints

14. Given an endpoint ( 3,5 ), and midpoint
( 6, -2 ), find the other endpoint.
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 ) =