Question

What is the answer to this question?

Answer 1

Perpendicular

Explanation:

Parallel lines have equal slopes.

The product of perpendicular slopes = - 1

Calculate the slopes of u and v using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 51, 65) and (x₂, y₂ ) = (- 46, 96)

m =
`(96-65)/(-46+51)` =
`(31)/(5)`

Repeat with (x₁, y₁ ) = (- 37, 85) and (x₂, y₂ ) = (- 6, 80)

m =
`(80-85)/(-6+37)` = -
`(5)/(31)`

Since
`(31)/(5)` × -
`(5)/(31)` = - 1

Then the lines are Perpendicular