Question

Which best describes the relationship between the line that passes through the points (–6, –1) and (–11, 1) and the line that passes through the points (–3, –8) and (–5, –13)?

Please answer due by tonight Thank You

Answer 1

The two are perpendicular to each other because the two slopes are negative reciprocals

(Y2 - Y1) / (X2 - X1)

First slope:
( 1 - (-1)) / (-11 - (-6))
2/-5

Second slope:
(-13 - (-8)) / (-5 - (-3))
-5/-2 or 5/2

You know when two aliens are perpendicular when you multiply the two slopes and get -1 as the product

-2/5 X 5/2 = -1

Thus the two lines are perpendicular to each other.

Answer 2

The lines are perpendicular

Explanation:

For a couple of points
`(x_1, y_1)` and
`(x_2, y_2)` the formula to calculate the slope of a line is:

`m=(y_2-y_1)/(x_2-x_1)`

If two lines are parallel then their slopes are equal, but if two lines of slopes
`m_1` and
`m_2` are perpendicular then it is true that:

`m_2=-(1)/(m_1)`

For the points (–6, –1) and (–11, 1) the slope of the line is:

`m_1=(1-(-1))/(-11-(-6))=-(2)/(5)`

For the points (–3, –8) and (–5, –13) the slope of the line is:

`m_2=(-13-(-8))/(-5-(-3))=(5)/(2)`

Note that
`m_2=-(1)/(m_1)`

So the lines are perpendicular