Question

question 1 of 5 select the correct answer. the vertices of quadrilateral abcd are a(0,-4), b(3,0), c(-6,4), and d(-3,8). what condition verifies the diagonals are perpendicular? the slopes of ac and bd are the same. the product of the slopes of ab and bd is 1. the lengths of ac and bd are the same. the product of the slopes of ac and bd is -1.

Explanation:

Step1: Recall slope - perpendicularity condition

If two lines are perpendicular, the product of their slopes is - 1. Diagonals of a quadrilateral are perpendicular when the product of their slopes is - 1.

Step2: Analyze given options

We are looking for the condition that verifies the diagonals are perpendicular. The correct condition is that the product of the slopes of the diagonals is - 1. In quadrilateral \(ABCD\), the diagonals are \(\overline{AC}\) and \(\overline{BD}\), and the condition for them to be perpendicular is that the product of the slopes of \(\overline{AC}\) and \(\overline{BD}\) is - 1.

Answer:

The product of the slopes of \(\overline{AC}\) and \(\overline{BD}\) is - 1.