Question

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint 1: (-10,6) midpoint: (7,-6)

Answer 1

The other end point is (24, -18)

Solution:

Given that,

Endpoint 1 is (-10, 6)

Midpoint is: (7, -6)

We have to find the other endpoint

The midpoint is given by formula:

$M(x, y) = (\frac{x_1+x_2}{2} , \frac{y_1 + y_2}{2})$

From given,

$M(x, y) = (7, -6)\\\\(x_1, y_1) = (-10, 6)\\\\(x_2, y_2) = ?$

Substituting the values we get,

$(7, -6) = (\frac{-10+x_2}{2} , \frac{6+y_2}{2})$

On comparing both sides we get,

$7 = \frac{-10+x_2}{2} \text{ and } -6 = \frac{6+y_2}{2}\\\\14 = -10 + x_2 \text{ and } -12 = 6 + y_2\\\\x_2 = 24 \text{ and } y_2 = -18$

Thus the other end point is (24, -18)