How do you find one endpoint of a segment if you are given the midpoint and the other endpoint? ?

Question

One endpoint is (5,7) and midpoint is (0,3) what is the other endpoint?

can you please explain the steps & Formula.

ty

Answer 1

The formula is in two parts.

The x coordinate of the midpoint, x(m), is:

x(m) = (x1 + x2)/2

where x1 and x2 are the two endpoints.

The y coordinate of the midpoint, y(m), is:

y(m) = (y1 + y2)/2

where y1 and y2 are the two endpoints.

Start with the formula for finding x, and plug in what you know:

0 = (5 + x2)/2

Cross-multiply:

(2)(0) = (5 + x2)

0 = 5 + x2

Subtract 5 from both sides:

-5 = x2

Repeat for the y-coordinate:

3 = (7 + y2)/2

Cross-multiply:

(2)(3) = (7 + y2)

6 = 7 + y2

Subtract 7 from both sides:

-1 = y2

The other endpoint is at (-5, -1)

Hope that helps!