Question

Given points A(3,-1), B(3, 1), C(2,-2), and D(5, -2), are segments AB and CD congruent?

a) Yes
b) No
c) Not enough information
d) Cannot be determined

Answer 1

To determine if segments AB and CD are congruent, we calculate their lengths using the distance formula. AB has a length of 2, and CD has a length of 3, hence they are not congruent.

Step-by-step explanation:

The question asks whether segments AB and CD are congruent. We can determine this by calculating the lengths of AB and CD using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2).

• For segment AB, the coordinates are A(3,-1) and B(3, 1). The length of AB is √((3 - 3)^2 + (1 - (-1))^2), which simplifies to √0 + √4, and thus AB has a length of 2.
• For segment CD, the coordinates are C(2,-2) and D(5, -2). The length of CD is √((5 - 2)^2 + (-2 - (-2))^2), which simplifies to √9 + √0, giving CD a length of 3.

Since segment AB has a length of 2 and segment CD has a length of 3, they are not congruent. Therefore, the answer is No, segments AB and CD are not congruent.