Question

I need help, please.​

Answer 1

Perpendicular

Explanation:

B. Their slopes (or gradients). To determine whether two lines on a plane are parallel or perpendicular, we need to examine what their slopes are. You can do this by using:
`m=(y_2-y_1)/(x_2-x_1)`.

So for the first line, it'll be:
`m_1 = (0-4)/(2-0) = (-4)/(2) = -2`

And for the second line, it'll be:
`m_2 = (2-3)/(-4-(-2))=(-1)/(-2) = (1)/(2)`

If two lines are parallel, their slopes will be the same. If two lines are perpendicular, one line's slope will be the negative reciprocal of the other; this means you can express the relationship between the two slopes
`m_a` and
`m_b` as
`m_a = (-1)/(m_b)`.

So we can see immediately the two lines aren't parallel, since the two slopes are different (one is -2 and the other is 1/2). However, they are perpendicular since if we do
`m_a = (-1)/(m_b)` where
`m_a = (1)/(2)` and
`m_b = -2`, we see that the equation is true (
`(1)/(2) = (-1)/(-2)`).