Coordinates of Point H in GH Line

[brackenwolf]

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

 

[MarkFL]

Hello and welcome to MHB! :D

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[soroban]

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.