Question

A quadrilateral is formed by points A(-1,1), B(2,2), C(3,0), and D(0,-1). Prove that ABCD is not a rectangle.

a) True
b) False

Answer 1

To prove that ABCD is not a rectangle, we can calculate the slopes of the sides and check if any pairs are not perpendicular.

Step-by-step explanation:

To prove that ABCD is not a rectangle, we need to show that at least one of the angles of the quadrilateral is not a right angle. To do this, we can calculate the slopes of the sides AB, BC, CD, and DA and check if they are perpendicular. If any pair of sides are not perpendicular, then ABCD is not a rectangle.

Let's calculate the slopes:

Slope of AB: (2-1) / (2-(-1)) = 1/3

Slope of BC: (0-2) / (3-2) = -2

Slope of CD: (-1-0) / (0-3) = -1/3

Slope of DA: (1-(-1)) / (-1-(-1)) = 1

Since the slopes of AB and CD are not negative reciprocals, they are not perpendicular. Hence, ABCD is not a rectangle.