Question

A quadrilateral is on a coordinate plane at points A(-3, 1) B(1, 4) C(5, 1) D(1, -2).

Which sides are congruent? (Select all that apply)

AB
BC
CD
AD

Answer 1

AB and CD.

Explanation:

To check if two sides of a quadrilateral are congruent, we need to find the length of each side. We can use the distance formula to calculate the length of each side:

AB = √[(1 - 4)^2 + (4 - 1)^2] = √(9 + 9) = 3√2

BC = √[(5 - 1)^2 + (1 - 4)^2] = √(16 + 9) = √25 = 5

CD = √[(1 - 1)^2 + (-2 - 1)^2] = √9 = 3

AD = √[(-3 - 1)^2 + (1 - (-2))^2] = √(16 + 9) = √25 = 5

Therefore, AB and CD have the same length and are congruent, while BC and AD have the same length and are congruent.

So the correct answer is AB and CD.