Question

Determine which lines, if any, are parallel or perpendicular. Explain.

Answer 1

Answer:

line a and b are parallel, there is no perpendicular lines

Step-by-step explanation:

Looking at the slope of each line, you can identify whether the lines are parallel, perpendicularlar, or neither.

When the slopes are the same, they are parallel.

When the slopes have opposite sign and numerator and denominator flipped, they are perpendicular. Ex. $\frac{a}{b}$ and $-\frac{b}{a}$ are perpendicular slopes.

Finding slope is using the formula: $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Line a has slope  $\frac{3-4}{4-0}$ = $-\frac{1}{4}$

Line b also has slope $-\frac{1}{4}$

Line c has slope 2

Since slope of line a and b are same, they are parallel.

Line c is not perpendicular to line a and b because the slope should have opposite sign and numerator and denominator flipped, which is 4 not 2.