Question

A square has the vertices at (- 2, 6), (6, 1), (1, - 7) , and (- 7, - 2) . At what point do the diagonals of the square intersect?

Answer 1

Intersection point is: (-1/2, -1/2)

Explanation:

Notice from the attached image of the points on the plane, that opposite vertices are for example:

(-2, 6) and (1, -7), and we know that in a square, the diagonals intersect dividing themselves in equal parts. So what we need to find is the midpoint of the segment that joins (-2, 6) and (1, -7) to find where the diagonals intersect.

We use the formula for the midpoint:

x-midpoint = (x1 + x2) / 2

y-midpoint = (y1 + y2) / 2

In the case of the points (-2, 6) and (1, -7) these become:

x-midpoint = (-2 + 1) /2 = -1/2

y-midpoint = (6 + -7) / 2 = -1/2