Question

In square GEOM, the coordinates of G are ( 2,-2) In the coordinates of O are (-4,2). Determine and state the coordinates of vertices E and M

Answer 1

The diagonals of a square bisect each other and meet at 90°. Therefore, the coordinates of crossing-point of the diagonals coincide with the coordinates of bisection point of GO, which can be found via averaging of coordinates of points G and O

and equal (-1,0).

The diagonals of a square are equal, so projection of GO to X axis must be equal to projection of EM to Y axis and vice versa.

Hence, the coordinates of E are (-1 - $\frac{GO_y}{2}$ ,0 - $\frac{GO_x}{2}$ ),

where $GO_y$ - the projection of GO to Y axis, that equals 4,

$GO_x$ - the projection of GO to X axis, that equals 6.

So, coordinates of E are (-3,-3).

The coordinates of M are (-1 + $\frac{GO_y}{2}$ , 0 + $\frac{GO_x}{2}$).

So, coordinates of M are (1,3).