Question

Using the slope formula, determine whether vec (AB) and vec (CD) are parallel, perpendicular, or neither for A(1,1),B(-1,-5),C(3,2), and D(6,1).

Answer 1

The slopes of vec (AB) and vec (CD) are different, so they are neither parallel nor perpendicular.

Step-by-step explanation:

To determine whether vec (AB) and vec (CD) are parallel, perpendicular, or neither, we can first find the slopes of the two vectors using the slope formula. The slope formula is given by m = (y2 - y1) / (x2 - x1). In this case, the coordinates of A and B are (1,1) and (-1,-5) respectively. So, the slope of vec (AB) is (1 - (-5)) / (1 - (-1)) = 6 / 2 = 3.

The coordinates of C and D are (3,2) and (6,1) respectively. So, the slope of vec (CD) is (2 - 1) / (3 - 6) = 1 / -3 = -1/3.

Since the slopes of the two vectors are different (3 and -1/3), vec (AB) and vec (CD) are neither parallel nor perpendicular.