Respuesta :
Answer: At point ([tex]-\frac{1}{2},-\frac{1}{2}[/tex])
Step-by-step 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) = [tex](\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]
The opposite vertices of the given square are (-2,6) and (1,-7).
So, the intersection is
(x,y) = [tex](\frac{-2+1}{2} ,\frac{6-7}{2})[/tex]
(x,y) = [tex](-\frac{1}{2},-\frac{1}{2} )[/tex]
The diagonals of square with vertices (-2,6)(6,1)(1,-7)(-7,-2) intersect at point [tex](-\frac{1}{2},-\frac{1}{2} )[/tex].
