1) The point midway between -7 and 5 is -1. 2) The point midway between (-3, 1) and (5, 4) is (1, 2.5). 3) The distance between points (1, 1) and (4, 5) is 5.

1. What point is midway between -7 and 5?
7 5 2
1
2 2

2. What point is midway between (-3, 1) and (5, 4)?
(1, 2.5)
3 5 2
x 1
2 2
1 4 5
y or 2.5
2 2

3. Pythagorean Theorem:
a 2 + b 2 = c2
c
4 2 + 5 2 = c2 4
16 + 25 = c2
41 = c2 5
c = 41

4. Find the distance between (1, 1) and (4, 5)
3 2 + 42 = c2
9 + 16 = c2 4
25 = c2
c= 5 3

5. Pythagorean Theorem:
a 2 + b 2 = c2
c 2 = a 2 + b2
c = a2 + b2

6. Find the distance between (-4, 3) and (1, -5)
(-4 – 1)2 + (3 – -5)2 = c2
(-5)2 + (8)2 = c2
25 + 64 = c2 5
89 = c2
c = 89
8

7. Find the distance between (5, 3) and (-2, -4)
(5 – -2)2 + (3 – -4)2 = c2
(7)2 + (7)2 = c2
49 + 49 = c2 7
98 = c2
c = 98 = 7 2
7