1. Sec 1-3
Concept: Use Midpoint and Distance Formulas
Objective: Given coordinates in a plane, find lengths of segments as measured by a s.g.

2. Example 1: Find the length of AB
One way would be to use the Pythagorean Thm.
a2+b2=c2 X Y A B C C 3
32+42=C2
9+16 = C2
25=C2
√25 = √C2
5 = C 4

3. Distance Formula: A B
(x2,y2) C
C2 = a2+b2
y2-y1
(x2,y1)
(x1,y1)
x2-x1

4. Distance Formula
If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B is

5. Example 2: Use the distance formula to find the length of ABY A B
(6,4)
(2,1)
AB = 5

6. Example 3: Find the length of the segment with end points A(3,-2) and B(-4,1)

7. Midpoint of a Segment: a point that divides the segment into 2 congruent segments (the middle)

8. Example 4: Find the midpoint of DE with endpoints D(3,5) and E(-4,0)
B. Find the midpoint of DE with endpoints D(-1,8) and E(2,-5)

9. Example 5:
The midpoint of XY is M(2,1). One endpoint is Y(-7,11). Find the coordinates of the other endpoint
B. The midpoint of XY is M(-7,8). One endpoint is Y(4,-6). Find the coordinates of the other endpoint

10. TODAY’S WORK