Question

Lydia graphed ΔDEF at the coordinates D (−2, −1), E (−2, 2), and F (0, 0). She thinks ΔDEF is a right triangle. Is Lydia's assertion correct?
Yes; the slopes of segment EF and segment DF are opposite reciprocals.
Yes; the slopes of segment EF and segment DF are the same.
No; the slopes of segment EF and segment DF are not opposite reciprocals.
No; the slopes of segment EF. and segment DF are not the same.

Answer 1

Answer:

No; the slopes of segment EF and segment DF are not opposite reciprocals.

Step-by-step explanation:

The slope between two points O(e, f) and X (g,h) is given as:

$slope\ of\ |OX|=\frac{h-f}{g-e}$

The slopes of segment EF and segment DF are given below:

$slope\ of\ |EF|=\frac{0-2}{0-(-2)}=-1\\\\slope\ of\ |DF|=\frac{0-(-2)}{0-(-1)}=2$

For triangle DEF to be a right triangle, DF and EF are supposed to be perpendicular to each other. Two line are said to be perpendicular if the product of their slope is -1, i.e the slope of one line is the negative reciprocal (opposite reciprocal) of the other line.

Since the slope of DF and EF are not opposite reciprocals,  ΔDEF is not a right triangle.