Question

Given points A(2, −4), B(-2, −4), C(3, 1), D(3, -3) Determine whether AB and CD are congruent.

A. AB and CD are congruent.
B. AB and CD are not congruent.
C. Only AB is congruent to CD.
D. Only BC is congruent to AD.

Answer 1

To determine whether AB and CD are congruent, find the lengths of AB and CD using the distance formula and compare them. Both AB and CD have a length of 4 units, so they are congruent.

Step-by-step explanation:

To determine whether AB and CD are congruent, we need to find the lengths of AB and CD, and compare them.

AB has endpoints A (2, -4) and B (-2, -4). We can use the distance formula to find the length of AB:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((-2 - 2)^2 + (-4 - (-4))^2)

d = sqrt((-4)^2 + (0)^2)

d = sqrt(16 + 0)

d = sqrt(16)

d = 4

CD has endpoints C (3, 1) and D (3, -3). Again, using the distance formula, we can find the length of CD:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((3 - 3)^2 + (-3 - 1)^2)

d = sqrt((0)^2 + (-4)^2)

d = sqrt(0 + 16)

d = sqrt(16)

AB and CD both have a length of 4 units, so they are congruent. Therefore, the correct answer is A. AB and CD are congruent.