Respuesta :
The question is incomplete. Here is the complete question.
Carla and Johan are working together to determine if quadrilateral CDEF coordinates C(2,3), D(1,2), E(4,1) and F(5,3) has a right angle.
Carla sets up the following equations:
[tex]m_{CD}=\frac{2-3}{1-2}[/tex]
[tex]m_{DE}=\frac{1-2}{4-1}[/tex]
Jonah stes up the follwoing equations:
[tex]m_{CD}=\frac{2-3}{1-2}[/tex]
[tex]m_{EF}=\frac{3-1}{5-4}[/tex]
Who is on track to get the correct answer and why?
(a) Carla is on the right track because she is finding the slopes of the opposite sides to check for right angles.
(b) Carla is on the right track because she is finding the slopes of consecutive sides to check for right angles.
(c) Johan is on the right track because she is finding the slopes of the opposite sides to check for right angles.
(d) Johan is on the right track because she is finding the slopes of consecutive sides to check for right angles.
Answer: (b) Carla is on the right track because she is finding the slopes of consecutive sides to check for right angles.
Step-by-step explanation: To check if two sides form a right angle using slope, we have to find the slope of two consecutives sides. If the slopes are opposite reciprocals, sides are perpendicular, which means they form right angle.
Observing the equations, we noticed Carla was calculating slope of segments CD and DE, which are adjacents. While, Johan was calculating slope for segments CD and EF, which are opposite.
So, the person who is on the write track is Carla because she is determining slope of two consecutive sides to check for right triangles.
