1-7: midpoint and distance in the coordinate plane
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1-7: Midpoint and Distance in the Coordinate Plane
Mean• Average• If you had test scores of 90 and 83, how would you
find your average? 90 83Average
2
86.5
Midpoint• To find the midpoint of a segment on a number line.
Midpoint of AB90 83
2
A B
9083
173
2 86.5
Number Line Midpoint Formula• On a number line, the coordinate of the
midpoint of the segment with endpoints a and b is: 2
a b
Midpoint in a Coordinate Plane
A(1,3)
B(6,8)
(6,3)
6 13.5
2
8 35.5
2
(3.5,5.5)
Coordinate Plane Midpoint Formula• In the coordinate plane, the midpoint of the segment
with endpoints (x1, y1) and (x2, y2) is: 1 2 1 2M ,2 2
x x y y
Ex. 1: Find the coordinates of the midpoint of with the endpoints A (2, 3) and B (-5, 7).
Ex. 2: The midpoint of has coordinates (3, 4). Point A has coordinates (-3, -2). Find the coordinates of B.
2 ( 5),
2M
2 ( 5)
2
AB
AB
,51.5 3 7
2
Distance
A B
To find the horizontal or vertical distance: 6 1 5AB
Apply same idea to finding distance on the Coordinate Plane:
A
B
1x 2x
1y
2y
Distance formula based on Pythagorean Theorem:
2 2 2a b c
a
bc
2 2c a b 2 2
2 1 2 1( ) ( )c x x y y
2 1a x x 2 1b y y
Distance Formula
The distance between two points and is:
1 1,A x y 2 2,B x y
2 22 12 1( ) ( )d yyxx
Ex. 3: Find the distance between each pair of points.a). (1, 2), (3, 4) b). (-1, -2), (-3, -4)
2 23 1 4 2d 2 2
3 ( 1) 4 ( 2)d
4 4d
8 2.83d 8 2.83d
4 4d
Homework: p. 54 #7-39 odd