Lydia graphed ΔLMN at the coordinates L (0, 0), M (2, 2), and N (2, - 1). She thinks ΔLMN is a right triangle. Is Lydia's assertion correct? Yes; the slopes of segment LM and segment LN are opposite reciprocals. No; the slopes of segment LM and segment LN are not opposite reciprocals. Yes; the slopes of segment LM and segment LN are the same. No; the slopes of segment LM and segment LN are not the same.

Question

Mathematics

Chandler Bridges

Today, 12:48

Lydia graphed ΔLMN at the coordinates L (0, 0), M (2, 2), and N (2, - 1). She thinks ΔLMN is a right triangle. Is Lydia's assertion correct? Yes; the slopes of segment LM and segment LN are opposite reciprocals. No; the slopes of segment LM and segment LN are not opposite reciprocals. Yes; the slopes of segment LM and segment LN are the same. No; the slopes of segment LM and segment LN are not the same.

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Davila · Answer 1

No; the slopes of segment LM and segment LN are not opposite reciprocals

Step-by-step explanation:

slope of LM: (2 - 0) / (2 - 0) = 1

slope of LN: (-1 - 0) / (2 - 0) = - 1/2

Two lines are perpendicular when the multiplication of their slopes is equal to negative one, that is, they are opposite reciprocals. In this case:

slope of LM*slope of LN = 1 * (-1/2) = - 1/2