THE D

ISTA

NCE FORMULA

AL G

EB

RA

1 C

P

WARM UP

Can the set of numbers represent the lengths of the sides of a right triangle?

4, 5, 6

HOMEWORK SOLUTIONS

P. 416-417 #1-13 odd, 21-24

1. 10 3. 2.2 5. 7.17. 5.7 9. 20 11. 66.113. a) 62+82=100 b) 5; 12; 7;

4121. Yes 22. No 23. No24. Yes

WITH A PARTNER

1.Graph the points A(-3, 4), B(1, 1), C(- 3, 1). Then connect the points with a ruler.

2.Find the lengths of AC and BC.

3.Triangle ABC is a right triangle. Use the Pythagorean theorem to write an equation relating AC, BC, and AB.

4.Substitue values for AC and BC in the equation you write in Question 3. Solve the equation to find AB.

THE DISTANCE FORMULA

The distance d between any two points (x1, y1) and (x2, y2) is

EXAMPLE

Find the distance between ( - 4, 5 ) and ( 4 , - 2 )

THE MIDPOINT FORMULA

The midpoint M of a line segment with endpoints A(x1, y1) and B(x2, y2) is

EXAMPLE

Find the midpoint of the segment from A(-1, 6) to B(5, 0)

HOMEWORK

P. 423 #4-9, 17-20

P. 434 #62-65