Question

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

Answer 1

Answer: At point (
`-(1)/(2),-(1)/(2)`)

Explanation: Diagonal is a line uniting two opposite points. In a square, the diagonals intersect in a 90° and bisect each other, i.e., divides each diagonal into two segments of the same length.

In other words, the diagonals of a square meet at their midpoint, which is found as the following:

(x,y) =
`((x_(1)+x_(2))/(2) ,(y_(1)+y_(2))/(2))`

The opposite vertices of the given square are (-2,6) and (1,-7).

So, the intersection is

(x,y) =
`((-2+1)/(2) ,(6-7)/(2))`

(x,y) =
`(-(1)/(2),-(1)/(2) )`

The diagonals of square with vertices (-2,6)(6,1)(1,-7)(-7,-2) intersect at point
`(-(1)/(2),-(1)/(2) )`.