Question

Lydia graphed ΔXYZ at the coordinates X (0, −4), Y (2, −3), and Z (2, −6). She thinks ΔXYZ is a right triangle. Is Lydia's assertion correct?
Yes; the slopes of segment XY and segment XZ are the same.
Yes; the slopes of segment XYand segment XZ are opposite reciprocals.
No; the slopes of segment XYand segment XZ are not the same.
No; the slopes of segment XYand segment XZ are not opposite reciprocals.

Answer 1

Answer:

Option (4)

Step-by-step explanation:

Vertices of the triangle are X(0, -4), Y(2, -3) and Z(2, -6).

Slope of XY ($m_{1}$) = $\frac{y-y'}{x-x'}$

                            = $\frac{-3+4}{2-0}$

                     ($m_{1}$) = $\frac{1}{2}$

Similarly, slope of XZ ($m_{2}$) = $\frac{-6+4}{2-0}$          

                                   ($m_{2}$) = (-1)

$m_{1}\times m_{2}=-\frac{1}{2}$

Which should be (-1) if XY and XZ are perpendicular to each other.

Now we can say that XY and XZ are not perpendicular.

Therefore, Lydia's assertion that ΔXYZ is a right triangle is not correct.

Option (4) will be the answer.