Question

The midpoint of a segment is(2,1) and one endpoint (8,7).find the coordinates of the other endpoint

Answer 1

Let $A=(8,7)$, $B=(x_B,y_B)$ and the midpoint $M=(2,1)$. We have:

$M=\left(\dfrac{x_A+x_B}{2},\dfrac{y_A+y_B}{2}\right)\\\\\\(2,1)=\left(\dfrac{8+x_B}{2},\dfrac{7+y_B}{2}\right)\\\\\\\begin{cases}\dfrac{8+x_B}{2}=2\qquad|\cdot2\\\\\dfrac{7+y_B}{2}=1\qquad|\cdot2\end{cases}\\\\\\ \begin{cases}8+x_B=4\\7+y_B=2\end{cases}\\\\\\\begin{cases}x_B=4-8\\y_B=2-7\end{cases}\\\\\\\boxed{\begin{cases}x_B=-4\\y_B=-5\end{cases}}$

Answer C.

Answer 2

Option C

Coordinates of other endpoint is (-4,-5)

Given :

Midpoint is (2,1)

End point is (8,7)

find the other endpoint

Explanation :

We apply midpoint formula

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} ) \\Let \; (x_1,y_1) \; is \; the \; other \; endpint\\one \; endpoint \; (8,7)\\(\frac{x_1+8}{2},\frac{y_1+ 7}{2})=(2,1)$

Set the x values  and solve for x1

$\frac{x_1+8}{2}=2 \\\\x_1+8=4\\Subtract \; 8\\x_1=-4\\\\\\ \frac{y_1+ 7}{2}=1 \\\\y_1+7=2\\y_1=-5$

So, other endpoint is (-4,-5)

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