Question

The slope of PQ¯¯¯¯¯ is 52 .

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:-
$slope \: of \: xy = \frac{ - 10 - ( - 5)}{4 - 2} = \frac{ - 5}{2}$
$slope \: of \: tu = \frac{7 - 2}{2 - 0} = \frac{5}{2}$
$slope \: of \: rs = \frac{ - 6 - ( - 4)}{8 - 3} = \frac{ - 2}{5}$
$slope \: of \: vw = \frac{9 - 5}{4 - 14} = \frac{4}{ - 10} = \frac{ - 2}{5}$
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.