Question

GH has a midpoint at M(5, 9). Point H is at (8,9). Find the coordinates of point G.

Answer 1

Coordinates of G: (2, 9)

Explanation:

`\textrm{Let\;} (x_G, y_G)` be the coordinates of point G,
`(x_H, y_H)` the coordinates of point H and
`(x_M, y_M)` the coordinates of point M

The midpoints formula is

`(x_(M), y_(M)) = \left(\frac {x_(G) + x_(H)} {2} , \frac {y_(G) + y_(G)} {2}\right)`

`x_(M) = \frac {x_(G) + x_(H)} {2} (1)`

Since we are given
`x_M \textrm{ and } x_H, \\\\` we can compute
`x_G` as follows

`x_(G) = 2x_(M) - x_(H)\\\\= 2*5-8\\\\= 10-2\\\\= 2`

`y_(M) = \frac {y_(G) + y_(H)} {2}`

`y_G = 2y_M - y_H\\\\= 2*9-9\\\\=9\\\\`

So the coordinates of G are (2, 9)