find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint

Question

midpoint (9,0) endpoint (12,3)

Answer 1

Use the midpoint formula

 

M = (  (x₁ + x₂) / 2  ,  (y₁ + y₂) / 2 )

 

(9, 0) = (  (x₁ + 12) / 2  ,   (y₁ + 3) / 2)

 

 

Break up this formula into two equations.

 

(x₁ + 12) / 2 = 9           and          (y₁ + 3) / 2 = 0

 

 

Solve for x₁ and y₁ from the equations.

Answer 2

Hi Anne Marie,

 

So, the formula for finding the midpoint of a segment given the coordinates of its endpoints is:

 

((x₁+ x2)/2, (y₁ +  y₂)/2   {Average of the x coordinates, average of the y coordinates}.

 

For this problem we know the coordinates of the midpoint along with one of the endpoints.

 

So the x coordinate of the midpoint (9) must equal (12 + x₂)/2.

 

That is:  9 = (12 + x₂)/2  Solve for x₂. Follow a similar pattern to find the y coordinate of the unknown endpoint.

Answer 3

The x's are 3 apart and the y's are 3 apart. The other endpoint is (9 - 3, 0 - 3), or (6,-3).