Coordinates of Point H in GH Line

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SUMMARY

The coordinates of point H in the line segment GH can be determined using the midpoint formula. Given point G at coordinates (-2, 8) and the midpoint at (5, -3), the coordinates of point H can be calculated by solving the equations derived from the midpoint formula: \(\frac{-2+x}{2} = 5\) and \(\frac{8+y}{2} = -3\). Solving these equations yields the coordinates of H as (12, -14).

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brackenwolf
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GH is a straight line.
the coordinates of G are (-2,8)
the midpoint of GH is (5,-3)
work out the coordinates of H
 
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brackenwolf said:
GH is a straight line.
the coordinates of G are (-2,8)
the midpoint of GH is (5,-3)
work out the coordinates of H
Formula
The midpoint of (x_1,y_1) and (x_2,y_2) is: \left(\frac{x_1+x_2}{2},\,\frac{y_1+y_2}{2}\right)

We are told that: the midpoint of G(-2,8) and H(x,y) is (5,-3).

Hence, we have: .\frac{-2+x}{2} \,=\,5,\quad \frac{8+y}{2} \,=\,-3

Solve the two equations.
 

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