How do you find the coordinates of the other endpoint of a segment with the given P = (5, 6) and midpoint M = (8, 2)?

Question

5430 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-05T12:00:58

See the entire solution process below:

The formula to find the mid-point of a line segment give the two end points is:

$M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)$

Where $M$ is the midpoint and the given points are:

$(color(red)((x_1, y_1)))$ and $(color(blue)((x_2, y_2)))$

Substituting the information we have from the problem gives:

$(8, 2) = ((color(red)(5) + color(blue)(x_2))/2 , (color(red)(6) + color(blue)(y_2))/2)$

First, we can solve for $x_2$ :

$8 = (5 + x_2)/2$

$color(red)(2) xx 8 = color(red)(2) xx (5 + x_2)/2$

$16 = cancel(color(red)(2)) xx (5 + x_2)/color(red)(cancel(color(black)(2)))$

$16 = 5 + x_2$

$-color(red)(5) + 16 = -color(red)(5) + 5 + x_2$

$11 = 0 + x_2$

$11 = x_2$

Next, we can solve for $y_2$

$2 = (6 + y_2)/2$

$color(red)(2) xx 2 = color(red)(2) xx (6 + y_2)/2$

$4 = cancel(color(red)(2)) xx (6 + y_2)/color(red)(cancel(color(black)(2)))$

$-color(red)(6) + 4 = -color(red)(6) + 6 + y_2$

$-2 = 0 + y_2$

$-2 = y_2$

The other end point is $(11, -2)$