Question

Lines MN and PQ are parallel. Lines RS and TV intersect them. Which statements are true about these lines? Check all that apply.

Answer 1

The correct answer is:
RS is perpendicular to MN and PQ.

Explanation:
We can use the slopes of these lines to determine the answer.
Slope is given by the formula
m=$\frac{y_{2}- y_{1} }{ x_{2} - x_{1} }$.

Using the coordinates for M and N, we have:
m=$\frac{3--1}{3--3} = \frac{4}{6} = \frac{2}{3}$.

Since PQ is parallel to MN, its slope will be $\frac{2}{3}$ as well, since parallel lines have the same slope.

Using the coordinates for points T and V in the slope formula, we have
m=$\frac{-4-1}{0--4} =- \frac{5}{4}$.

This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.

Using the coordinates for R and S in the slope formula, we have
m=$\frac{-2-1}{2-0} =- \frac{3}{2}$. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.

Answer 2

The slope of line MN is 2/3.

The slope of line RS is -3/2

Lines RS is perpendicular to both line MN and line PQ.