Question

Tell whether the intersection of AB and CD forms a right angle.

A(7, 12), B(1, 5), C(10, -7), D(3, -1)
Option 1: Yes
Option 2: No

Answer 1

The intersection of line segments AB and CD forms a right angle because the slopes of AB and CD are negative reciprocals of each other.

Step-by-step explanation:

To determine whether the intersection of line segments AB and CD forms a right angle, we need to find the slopes of the line segments and see if they are negative reciprocals of each other. The slope of a line segment between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).

The slope of AB is (5 - 12) / (1 - 7) = -7 / -6 = 7/6, and the slope of CD is (-1 - (-7)) / (3 - 10) = 6 / -7 = -6/7. Since the slopes are negative reciprocals of each other, the line segments AB and CD do intersect at a right angle. Therefore, the answer is Option 1: Yes, they form a right angle.