The midpoint of $ \overline{GH} $ is $ M(-6, -3) $. One endpoint is $ H(-4, 4) $. Find the...

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The midpoint of $ \overline{GH} $ is $ M(-6, -3) $. One endpoint is $ H(-4, 4) $. Find the coordinates of endpoint G. a $ (1, 3.5) $ b $ (-5, 0.5) $ c $ (-8, -10) $ d $ (-2, 11) $

SnapAndSolve AI · Accepted Answer

To find the coordinates of endpoint G, use the midpoint formula:

Midpoint formula: $ M(x, y) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $

Given $ M(-6, -3) $ and $ H(-4, 4) $, let $ G(x, y) $ be the coordinates of endpoint G.

For the x-coordinate: $ -6 = \frac{-4 + x}{2} $
Solving for $ x $:
$ -12 = -4 + x $
$ x = -8 $
For the y-coordinate: $ -3 = \frac{4 + y}{2} $
Solving for $ y $:
$ -6 = 4 + y $
$ y = -10 $

Therefore, the coordinates of endpoint G are $ (-8, -10) $, which corresponds to option c.

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The midpoint of \( \overline{GH} \) is \( M(-6, -3) \). One endpoint is \( H(-4, 4) \). Find the...

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