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 a right angle. carla sets up the following equations: $m_{cd}=\frac{2 - 3}{1 - 2}$, $m_{de}=\frac{1 - 2}{4 - 1}$. jonah sets up the following equations: $m_{cd}=\frac{2 - 3}{1 - 2}$, $m_{ef}=\frac{3 - 1}{5 - 4}$. who is on track to get the correct answer, and why? carla is on the right track because she is finding the slopes of the opposite sides to check for right angles. carla is on the right track because she is finding the slopes of consecutive sides to check for right angles. jonah is on the right track because he is finding the slopes of the opposite sides to check for right angles. jonah is on the right track because he is finding the slopes of consecutive sides to check for right angles.

Explanation:

Step1: Recall slope - perpendicularity rule

Two lines are perpendicular (form a right - angle) if the product of their slopes is - 1. To check for right - angles in a quadrilateral, we need to find the slopes of consecutive sides.

Step2: Analyze Carla's equations

Carla calculates \(m_{CD}=\frac{2 - 3}{1 - 2}\) (slope of line segment CD with \(C(2,3)\) and \(D(1,2)\)) and \(m_{DE}=\frac{1 - 2}{4 - 1}\) (slope of line segment DE with \(D(1,2)\) and \(E(4,1)\)). She is finding the slopes of consecutive sides.

Step3: Analyze Jonah's equations

Jonah calculates \(m_{CD}=\frac{2 - 3}{1 - 2}\) and \(m_{EF}=\frac{3 - 1}{5 - 4}\). EF is not a consecutive side to CD.

Answer:

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