The midpoint of A B is at ( 3 , 3 ) . If A = ( − 8 , 7 ) , find B .

Answer 1

A quick way to do this is to just think to yourself from -8 to 3 is +11, so just add 11 to 3 and get 14.

And from 7 to 3 is down 4 so just subtract 4 from 3 and get -1.

So B = (14,-1)

Or you can use the midpoint formula

3 = (-8 + x)/2

x = 14

3 = (7 + y)/2

y = -1

Answer 2

Given two points (x₁, y₁) and (x₂, y₂), the midpoint is:

So given that x₁ = -8 and the x-coordinate of the midpoint is 3, we can say:

(-8 + x₂)/2 = 3

(-8 + x₂) = 3(2)

-8 + x₂ = 6

x₂ = 14

And given that y₁ = 7 and the y-coordinate of the midpoint is 3, we can say:

(7 + y₂)/2 = 3

(7 + y₂) = 3(2)

7 + y₂ = 6

y₂ = -1

So B is (14, -1)

Answer 3

B is (14, -1)

(3,3) is equidistant from A and B