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.

The true statement is (d) No; the slopes of segment XY and segment XZ are not opposite reciprocals.

The coordinates are given as:

X = (0,-4)

Y = (2,-3)

Z = (2,-6)

Start by calculating the slopes of XY and XZ using:

So, we have:

Also, we have:

For the shape to be a right-angle triangle, then:

So, we have:

The above equation is false.

Hence, the triangle is not a right-angled triangle

Read more about right-angled triangles at:

link

Option (4)

Step-by-step explanation:

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

Slope of XY () =

                            =

                     () =

Similarly, slope of XZ () =          

                                   () = (-1)

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.