Question

Find the coordinates of the other endpoint of the? segment, given its midpoint and one endpoint.? (Hint: Let? (x,y) be the unknown endpoint. Apply the midpoint? formula, and solve the two equations for x and? y.) midpoint ?( negative 11 ?11?, 18 18?), endpoint ?( negative 5 ?5?, 10 10?)

Answer 1

We are given mid-point (-11, 18).

One end point (-5, 10).

$\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)$

Let us take coordinate of other end points is (x,y).

Therefore,

$\left(x_1,\:y_1\right)=\left(-5,\:10\right),\:\left(x_2,\:y_2\right)=\left(x,\:y\right)$

$\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right) =\left(\frac{x-5}{2},\:\frac{y+10}{2}\right)$

Given mid point (-11, 18).

Therefore,

$\left(\frac{x-5}{2},\:\frac{y+10}{2}\right) = (-11, 18)$

$\frac{x-5}{2}=-11$ and $\frac{y+10}{2} = 18$

Multiplying both sides by 2 in both equations, we get

x-5 = -22 and y+10 =36.

x = -22+5 and y = 36-10

x = -17 and y = 26.

Therefore, corrdinates of other end point is (-17, 26).