Lydia graphed ADEF at the coordinates D (-2,-1), E (-2, 2), and F (0,0). She thinks ADEF is a right triangle. Is Lydia's asserti

Question

2 years ago

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Lydia graphed ADEF at the coordinates D (-2,-1), E (-2, 2), and F (0,0). She thinks ADEF is a right triangle. Is Lydia's asserti

on correct?
A) Yes, the slopes of EF and DF are opposite reciprocals.
B) Yes, the slopes of EF and DF are the same.
C) No, the slopes of EF and DF are not opposite reciprocals.
D) No, the slopes of EF and DF are not the same.

Mathematics

2 answers:

Setler79 [48] · Answer 1 · 2023-04-16T13:55:42+03:00

The true statement is (c) No; the slopes of segment EF and segment DF are not opposite reciprocals.

<h3>Right triangles </h3>

Right triangles have a pair of perpendicular lines

Coordinates

The coordinates are given as:

D = (-2,-1)
E = (-2,2)
F = (0,0)

<h3>Slopes</h3>

Start by calculating the slopes of lines DF and EF using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m_{DF} = \frac{0 + 1}{0 +2}$

$m_{DF} = \frac{1}{2}$

Also, we have:

$m_{EF} = \frac{0 -2 }{0+2}$

$m_{EF} = \frac{-2 }{2}$

$m_{EF} = -1$

For the triangle to be a right triangle, then the calculated slopes must be opposite reciprocals.

i.e.

$m_1 = -\frac{1}{m_2}$

By comparison, the slopes of both lines are not opposite reciprocals.

Hence, the true statement is (c)