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

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

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

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 = (6 - 0)/(2 - 4) = (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 = (6 - 7)/(5 - 8) = (-1)/(-3) = (1)/(3)`

This is a perpendicular to MN, not a parallel.

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

`S = (3 - 2)/(1 - 4) = (1)/(-3)`

Not parallel, nor perpendicular.

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

`S = (1 - 10)/(8 - 5) = (-9)/(3) = -3`

So, TU is also parallel to MN