Question

The midpoint of \overline{\text{AB}}

AB
is M(5, 6)M(5,6). If the coordinates of AA are (3, 8)(3,8), what are the coordinates of BB?

Answer 1

Answer: (7, 4)

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Step-by-step explanation:

Point B is at the location (x, y)

The x coordinates of A and B are 3 and x respectively. Add them up, divide in half, and set the result equal to the x coordinate of M which is 5

(3+x)/2 = 5

3+x = 2*5

3+x = 10

x = 10-3

x = 7 which is the x coordinate of point B

Repeat this same idea for the y coordinates.

(8+y)/2 = 6

8+y = 2*6

8+y = 12

y = 12-8

y = 4

Therefore, point B is located at (x,y) = (7, 4)

Visual verification is shown below. You could also use the midpoint formula on segment AB to find that M = (5,6) is the midpoint.