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.

Question

Mathematics

Johnathon Whitehead

21 May, 00:22

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.

+1

Answers (1)

Know the Answer?

Randall Ewing · Answer 1

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

Step-by-step explanation:

D (-2, - 1), E (-2, 2), and F (0, 0).

slopes of segment EF = (yF - yE) / (xF - xE) = (0 - 2) / (0 - (-2)) = - 1

slopes of segment DF = (yF - yD) / (xF - xD) = (0 - (-1)) / (0 - (-2)) = 1/2

If the multiplication of the slopes is equal to - 1, then they are opposite reciprocals and the triangle is a right triangle

slopes of segment EF * slopes of segment DF = - 1 * 1/2 = - 1/2 ≠ - 1