Find the missing endpoint. given the other endpoint and midpoint.

Question

Endpoint: (8,6)

Midpoint: (-2,7)

Answer 1

(8 + x) / 2 = -2

(6 + y) / 2 = 7

 

Can you solve for x and y?

Answer 2

Endpoint: (8,6)
Midpoint: (-2,7)

 

We can do this a couple of ways.  The easiest is probably to apply the

same changes in (x, y) to the midpoint as we did in getting from the

1st endpoint to the midpoint.

x went from 8 to -2 which is a drop of 10 or -10

y went from 6 to 7 which is a raise of 1 or +1

 

From the midpoint go left 10 and up 1

 (-2-10, 7+1) = (-12, 8)

 

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From the midpoint formula: 

Midpoint of (x₁, y₁), (x₂, y2) is  ((x₁+x₂)/2, (y₁ + y₂)/2)

 

(8+x₂)/2 = -2  

8 + x₂ = -4

x₂ = -12

 

(6+y₂)/2 = 7

6 + y₂ = 14

 = 8

 

New endpoint:  (-12, 8)