Question

The midpoint of a segment is 19,5) and one of the endpoints is (13,81 What are the coordinates of the otherendpoint

Answer 1

Answer:

$(25,-71)$

Step-by-step explanation:

Given

$(x,y) = (19,5)$ --- midpoint

$(x_1,y_1) = (13,81)$ --- end 1

Required

The other endpoint

Using midpoint formula, we have:

$(x,y) = 0.5 * [x_1 + x_2, y_1 + y_2]$

So, we have:

$(19,5) = 0.5 * [13 + x_2, 81 + y_2]$

Multiply both sides by 2

$2 * (19,5) = 2 * 0.5 * [13 + x_2, 81 + y_2]$

$(38,10) = [13 + x_2, 81 + y_2]$

By comparison:

$x_2 + 13 = 38$ and $y_2 + 81 = 10$

So:

$x_2 = 38 - 13$

$x_2 = 25$

and

$y_2 = 10 - 81$

$y_2 = - 71$

Henc, the other endpoint is:

$(25,-71)$