Question

the slope of mn is -3

Which segment are parallel to mn

Select each correct answer.

Answer 1

keeping in mind that any line parallel to MN will have the same exact slope as MN's.

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-6}{4-2}\implies \cfrac{-6}{2}\implies \cfrac{-3}{1}\implies -3~~\checkmark \\\\[-0.35em] ~\dotfill$

$\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-1}{5-8}\implies \cfrac{9}{-3}\implies \cfrac{3}{-1}\implies -3~~\checkmark$

Answer 2

Answer:

WX (2,6) and (4,0)

TU (8,1) and (5,10)

Step-by-step explanation:

We just need to calculate the slope of each of the possible answers and we'll know which is parallel. To be parallel, the other slope also has to be -3.

To calculate the slope, we do the difference of Y values over the difference X values.

WX (2,6) and (4,0)

$S = \frac{6 - 0}{2 - 4} = \frac{6}{-2}=-3$

This slope is -3, so we have one right answer already, let's look for another.

PQ (5,6) and (8,7)

$S = \frac{6 - 7}{5 - 8} = \frac{-1}{-3} = \frac{1}{3}$

This is a perpendicular to MN, not a parallel.

RS (1,3) and (4,2)

$S = \frac{3 - 2}{1 - 4} = \frac{1}{-3}$

Not parallel, nor perpendicular.

TU (8,1) and (5,10)

$S = \frac{1 - 10}{8 - 5} = \frac{-9}{3} = -3$

So, TU is also parallel to MN