Question

One line passes through the points \blueD{(-3,-1)}(−3,−1)start color #11accd, (, minus, 3, comma, minus, 1, ), end color #11accd and \blueD{(1,-9)}(1,−9)start color #11accd, (, 1, comma, minus, 9, ), end color #11accd. Another line passes through points \greenD{(1,4)}(1,4)start color #1fab54, (, 1, comma, 4, ), end color #1fab54 and \green{(5,6)}(5,6)start color #1fab54, (, 5, comma, 6, ), end color #1fab54. Are the lines parallel, perpendicular, or neither?

Answer 1

Answer:

The lines are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

Remember that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Find the slope of the first line

we have the points

(-3,-1) and (1,-9)

substitute in the formula

$m_1=\frac{-9+1}{1+3}$

$m_1=\frac{-8}{4}$

$m_1=-2$

Find the slope of the second line

we have the points

(1,4) and (5,6)

substitute in the formula

$m_2=\frac{6-4}{5-1}$

$m_2=\frac{2}{4}$

Simplify

$m_2=\frac{1}{2}$

Compare the slopes

$m_1=-2$

$m_2=\frac{1}{2}$

Find out the product

$m_1*m_2=(-2)(\frac{1}{2})=-1$

therefore

The lines are perpendicular

Answer 2

Answer:

Perpendicular

Step-by-step explanation: