Simplify the expression
2 answers:
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Answer:
3/4
Step-by-step explanation:
First of all, we need to calculate the slope of the line shown. This can be computed as:
where
is the increment along the y-direction
is the increment along the x-direction
We can choose the following two points to calculate the slope of the line shown:
(-3,2) and (0,-2)
And so, the slope of the line shown is
Two lines are said to be perpendicular if the slope of the first line is the negative reciprocal of the slope of the second line:
Using , we find that a line perpendicular to the line shown should have a slope of
We can rewrite the expression under the radical as
then taking the fourth root, we get
Why the absolute value? It's for the same reason that
since both and
return the same number
, and
captures both possibilities. From here, we have
The absolute values disappear on all but the term because all of
,
and
are positive, while
could potentially be negative. So we end up with