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: 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?
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.) Jonah is on the right track because he is finding the slopes of the opposite sides to check for right angles.
D.)Jonah is on the right track because he is finding the slopes of consecutive sides to check for right angles.

Answer 1

Answer:

Option (B)

Step-by-step explanation:

CDEF is a quadrilateral having vertex C(2, 3), D(1, 2), E(4, 1), F(5, 3).

To prove that the given quadrilateral has a right angle, we will use the property of perpendicular lines.

$m_1\times m_2=-1$

where $m_1$ and $m_2$ are the slopes of the consecutive sides of the quadrilateral.

Since CD and DE are the consecutive sides of the quadrilateral, Carla is on the right track by finding the slopes of CD and DE.

Since Jonah is finding the slopes of opposite sides so he will not be able to use the property of perpendicular lines.

Option (B) will be the answer.