1. All slides in this chapter contain: Digital juice item #2F060_A_BonusDrop

2. Distance Formula
d = √ (x1 – x2)2 + (y1 – y2)2, where d is the distance between the points (x1, y1) and (x2, y2).

3. Example 1 Find the distance between the points (– 3, 5) and (2, – 6).
d = √ (x1 – x2)2 + (y1 – y2)2
= √ (– 3 – 2)2 + [5 – (– 6)]2
= √ (– 5)
= √ 146
≈ 12.1 units

4. A
(x1, y1)
All slides in this chapter contain: Digital juice item #2F060_A_BonusDrop C B
(x1, y2)
(x2, y2)

5. Midpoint Formula
The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is ,
x1 + x2 2
y1 + y2

6. Example 2
Find the midpoint of the segment extending from (– 8, – 2) to (– 1, 5).
– 8 + (– 1) 2 – , =
– 9 2
3 2 ,
= (– 4.5, 1.5)

7. Example 3
Parallelogram ABCD has vertices at A (3, 0), B (7, 1), C (7, 4), and D (3, 3). Find the length of each side and the midpoint of each diagonal.

8. AD = y1 – y2
= 3 – 0
= 3 units
BC = y1 – y2
= 4 – 1
= 3 units
CD = √ (7 – 3)2 + (4 – 3)2
= √
= √ 17
≈ 4.1 units
AB = √ (7 – 3)2 + (1 – 0)2
= √
= √ 17
≈ 4.1 units

9. Midpoint of AC , = =
10 2
4 2 ,
= (5, 2)
Midpoint of BD , = =
10 2
4 2 ,
= (5, 2)

10. Example
Find the distance between the points (– 1, 6) and (2, 4).
√ 13

11. Example
Find the midpoint of the segment extending from (4, 7) to (10, 13).
(7, 10)

12. Example
If (– 4, 5) is one endpoint of a line segment with midpoint (3, – 2), what is the other endpoint?
(10, – 9)

13. Example
Graph an isosceles triangle with vertices at (0, 0), (8, 0), and (4, 6). Find the midpoint of each side of the triangle.
(4, 0), (2, 3), (6, 3)

14. Example
Graph an isosceles triangle with vertices at (0, 0), (8, 0), and (4, 6). Is the figure formed by joining the midpoints similar to the original triangle?
yes

15. Exercise
Use the distance formula to find the lengths of the diagonals AC and BD of rectangle ABCD, whose vertices are A (– 1, 4), B (7, – 2), C (4, – 6), and D (– 4, 0). How do these two lengths compare?