The true statement is (c) No; the slopes of segment EF and segment DF are not opposite reciprocals.
Right triangles
Right triangles have a pair of perpendicular lines
Coordinates
The coordinates are given as:
- D = (-2,-1)
- E = (-2,2)
- F = (0,0)
Slopes
Start by calculating the slopes of lines DF and EF using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{DF} = \frac{0 + 1}{0 +2}[/tex]
[tex]m_{DF} = \frac{1}{2}[/tex]
Also, we have:
[tex]m_{EF} = \frac{0 -2 }{0+2}[/tex]
[tex]m_{EF} = \frac{-2 }{2}[/tex]
[tex]m_{EF} = -1[/tex]
For the triangle to be a right triangle, then the calculated slopes must be opposite reciprocals.
i.e.
[tex]m_1 = -\frac{1}{m_2}[/tex]
By comparison, the slopes of both lines are not opposite reciprocals.
Hence, the true statement is (c)
Read more about right triangles at:
https://brainly.com/question/17972372
