Question

The slope of PQ¯¯¯¯¯ is 52 .

Which segments are perpendicular to PQ¯¯¯¯¯ ?

Select each correct answer.

Answer 1

Slopes of perpendicular segments are always negative reciprocal of each other. Or, we can say product of slopes of perpendicular segments is always -1.
Given the slope of PQ is 5/2.
So the slope of its perpendicular segment should be -2/5.
Finding slopes of given options:-

`slope \: of \: xy = ( - 10 - ( - 5))/(4 - 2) = ( - 5)/(2)`

`slope \: of \: tu = (7 - 2)/(2 - 0) = (5)/(2)`

`slope \: of \: rs = ( - 6 - ( - 4))/(8 - 3) = ( - 2)/(5)`

`slope \: of \: vw = (9 - 5)/(4 - 14) = (4)/( - 10) = ( - 2)/(5)`
From above calculations, it is clearly visible that slopes of RS and VW are negative reciprocal of slope of PQ.

So, correct answers are RS and VW.