Question

Use AB and CD to answer the question.

AB contains the points A(2, 1) and B(3, 4).
CD contains the points C(-2, -1) and D(1, -2).
Is AB perpendicular to CD? Why or why not?
a) Yes, because the slopes of AB and CD are opposite reciprocals.
b) Yes, because the slopes of AB and CD are equal.
c) No, because the slopes of AB and CD are opposite reciprocals.
d) No, because the slopes of AB and CD are parallel.

Answer 1

AB is not perpendicular to CD because the slopes of AB and CD are neither equal nor opposite reciprocals.

Step-by-step explanation:

To determine whether AB is perpendicular to CD, we need to compare the slopes of the two lines. The slope of a line can be found using the formula: slope = (change in y)/(change in x). For line AB, the slope is (4-1)/(3-2) = 3/1 = 3. For line CD, the slope is (-2-(-1))/(1-(-2)) = -1/3. The slopes of AB and CD are neither equal nor opposite reciprocals. Therefore, AB is not perpendicular to CD. The correct answer is c) No, because the slopes of AB and CD are opposite reciprocals.