Question

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?.

Answer 1

No product results in -1, hence δlmn is NOT a right triangle showing that  lydia's assertion is incorrect

Perpendicular lines

In order to determine whether triangle lmn  is right-angled, we need to determine the slope of lm, ln, and mn first as shown:

For the slope of lm:

$m_{lm} = \frac{2-0}{2-0}\\ m_{lm} =2/2\\m_{lm} =1$

For the slope of ln:

$m_{ln} = \frac{-1-0}{2-0}\\m_{ln} =-1/2$

For the slope of mn:

$m_{mn} = \frac{-1-2}{2-2}\\m_{ln} =-3/0 = \infty$

• If any of the two lines is perpendicular, hence the triangle lmn is right-angled.

• To check, we will take the product of the slopes and see if it is equivalent to -1.

Product of slope lm and ln

$m_{lm}\times m_{ln} = 1 \times -1/2\\m_{lm}\times m_{ln} = -1/2$

Since no product results in -1, hence δlmn is NOT a right triangle showing that  Lydia's assertion is incorrect

Learn more on slopes here: brainly.com/question/3493733

Answer 2

Answer:

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

Explanation: