Question

given the midpoint and one endpoint of a line segment, find the other endpoint. endpoint: (4, 10) midpoint: (5, 9)

Answer 1

The answer is (6, 8).

EXPLANATION

If you are given two numbers, you can find the number exactly between them by averaging them, by adding them together and dividing by two. The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.

That is:

$( \frac{x1 + x2}{2}. \frac{y1 + y2}{2} )$

But since the midpoint is given, we'll work this out in a different way.

To find the x of the other endpoint or x2, we'll have first to plug-in the given x values in the midpoint and x1.

So,

$m = \frac{x1 + x2}{2} \\ 5= \frac{4 + x2}{2}\\ 10= 4 + x2 \\ x2 = 6$

Now, let's proceed to y2.

$m = \frac{y1 + y2}{2} \\ 9= \frac{10 + y2}{2}\\ 18= 10 + y2 \\ y2 = 8$

So now you have the x and y values of the other endpoint: (6,8).