Answer:
Quadrilateral ABCD is not a square. The product of slopes of its diagonals is not -1.
Explanation:
Point A is (-4,6)
Point B is (-12,-12)
Point C is (6,-18)
Point D is (13,-1)
Given that the diagonals of a square are perpendicular to each other;
We know that the product of slopes of two perpendicular lines is -1.
So, slope(m) of AC × slope(m) of BD should be equal to -1.
Slope of AC = (Change in y-axis) ÷ (Change in x-axis) = (-18 - 6) ÷ (6 - -4) = -24/10 = -2.4
Slope of BD = (Change in y-axis) ÷ (Change in x-axis) = (-1 - -12) ÷ (13 - -12) = 11/25 = 0.44
The product of slope of AC and slope of BD = -2.4 × 0.44 = -1.056
Since the product of slope of AC and slope of BD is not -1 hence AC is not perpendicular to BD thus quadrilateral ABCD is not a square.