1. The Distance and Midpoint Formulas
Topic 7.1

2. Distance Formula
Used to find the distance between two points

3. Example
Find the distance between A(4,8) and B(1,12)
A (4, 8)
B (1, 12)

4. YOU TRY!! Find the distance between: A. (2, 7) and (11, 9)
B. (-5, 8) and (2, - 4)

5. YOU TRY!! Find the distance between: A. (2, 7) and (11, 9)
B. (-5, 8) and (2, - 4)

6. Midpoint Formula
Used to find the center of a line segment

7. Example
Find the midpoint between A(4,8) and B(1,12)
A (4, 8)
B (1, 12)

8. YOU TRY!! Find the midpoint between: A) (2, 7) and (14, 9)
B) (-5, 8) and (2, - 4)

9. YOU TRY!! Find the midpoint between: A) (2, 7) and (14, 9)
B) (-5, 8) and (2, - 4)

10. What is a right triangle?
hypotenuse
leg
right angle
leg
It is a triangle which has an angle that is 90 degrees.
The two sides that make up the right angle are called legs.
The side opposite the right angle is the hypotenuse.

11. Note: The hypotenuse, c, is always the longest side.
The Pythagorean Theorem
In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then
a2 + b2 = c2
Note: The hypotenuse, c, is always the longest side.

12. Find the length of the hypotenuse if 1. a = 12 and b = 16.

13. square root of both sides
= c2
= c2
400 = c2
square root of both sides
20 = c

14. Find the length of the leg, to the nearest hundredth, if a = 4 and c = 10.

15. 42 + b2 = 102
16 + b2 = 100
Solve for b.
b2 =
b2 = 84
b = 9.17