Question

Find the coordinates of G if F(2,5) is the midpoint of line GJ and J and has coordinates (-2,8)

Answer 1

G(6,2)

Explanation:

If point
`F(x_F,y_F)` is the midpoint of the segment GJ, where
`G(x_G,y_G)` and
`J(x_J,y_J)`, then

`x_F=(x_G+x_J)/(2),\\ \\y_F=(y_G+y_J)/(2).`

In your case,

`F(2,5),\ J(-2,8),`

therefore,

`2=(x_G+(-2))/(2),\\ \\5=(y_G+8)/(2).`

Thus,

`x_G-2=4\Rightarrow x_G=6,\\ \\y_G+8=10\Rightarrow y_G=2.`