What is the midpoint of a segment whose endpoints are (9, -9) and (-3, 7)?

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Answer 1 · 2016-12-02T13:26:56

$(3, - 1)$ $(3,-1)$

We need to find the midpoint of $(9, - 9) and (- 3, 7)$ $(9,-9) and (-3,7)$

For that, we use the midpoint formula

$Midpoint formula = (x, y) = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $color(blue)("Midpoint formula"=(x,y)=((x_1+x_2)/2,(y_1+y_2)/2)$

( $x and y$ $x and y$ are the points of the midpoint)

We know that,

$(9, - 9) = (x_{1}, y_{1})$ $color(orange)((9,-9)=(x_1,y_1)$

$(- 3, 7) = (x_{2}, y_{2})$ $color(orange)((-3,7)=(x_2,y_2)$

So the midpoint is

$\to (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $rarr((x_1+x_2)/2,(y_1+y_2)/2)$

$\to (\frac{9 + (- 3)}{2}, \frac{- 9 + 7}{2})$ $rarr((9+(-3))/2,(-9+7)/2)$

$\to (\frac{6}{2}, \frac{- 2}{2})$ $rarr((6)/2,(-2)/2)$

$\Rightarrow (3, - 1)$ $color(green)(rArr(3,-1)$

Therefore, the midpoint is $(3, - 1)$ $(3,-1)$