Question

Carla and Jonah are working together to determine if quadrilateral CDEF with coordinates C(2, 3), D(1, 2), E(4, 1), and F(5, 3) has perpendicular sides.

Carla sets up the following equations:
slope of segment CD equals 2 minus 3 all over 1 minus 2
slope of segment DE equals 1 minus 2 all over 4 minus 1

Jonah sets up the following equations:
slope of segment CD equals 2 minus 3 all over 1 minus 2
slope of segment EF equals 3 minus 1 all over 5 minus 4

Who is on track to get the correct answer, and why?

Group of answer choices

Carla is on the right track because she is finding the slopes of consecutive sides to check for perpendicular sides.

Carla is on the right track because she is finding the slopes of the opposite sides to check for perpendicular sides.

Jonah is on the right track because he is finding the slopes of the opposite sides to check for perpendicular sides.

Jonah is on the right track because he is finding the slopes of consecutive sides to check for perpendicular sides.

Answer 1

Carla is on the right track as she is correctly finding the slopes of consecutive sides CD and DE to determine if they form perpendicular sides. Jonah's approach is incorrect as he compares the slopes of non-consecutive sides CD and EF which doesn't ascertain perpendicularity between adjacent sides. The correct answer is option b.

Step-by-step explanation:

To determine if quadrilateral CDEF has perpendicular sides, we must calculate the slopes of consecutive sides and check if the product of their slopes is -1. This is because two lines are perpendicular if the product of their slopes is -1. Let's evaluate the setups that Carla and Jonah have made.

Carla's setup:

• Slope of segment CD = (2 - 3) / (1 - 2) = -1 / -1 = 1
• Slope of segment DE = (1 - 2) / (4 - 1) = -1 / 3

Jonah's setup:

• Slope of segment CD = (2 - 3) / (1 - 2) = -1 / -1 = 1
• Slope of segment EF = (3 - 1) / (5 - 4) = 2 / 1 = 2

Since we are looking for perpendicularity, we need the slopes of consecutive sides. Carla is comparing the slopes of segments CD and DE which are consecutive sides, while Jonah is comparing non-consecutive sides, CD and EF. Therefore, Carla is on the right track because she is finding the slopes of consecutive sides to check for perpendicular sides.