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Example Question #2 : How To Find Out If Lines Are Perpendicular
Line , which follows the equation
, intersects line
at
. If line
also passes through
, are
and
perpendicular?
Yes, because the product of their slopes is not .
No, because the product of their slopes is
No, because the product of their slope is not .
Yes, because the product of their slopes is .
Yes, because the product of their slopes is .
The product of perpendicular slopes is always . Knowing this, and seeing that the slope of line
is
, we know any perpendicular line will have a slope of
.
Since line passes through
and
, we can use the slope equation:
Since the two slopes' product is , the lines are perpendicular.
Example Question #3 : How To Find Out If Lines Are Perpendicular
Are the following two lines perpendicular:
and
For two lines to be perpendicular they have to have slopes that multiply to get . The slope is found from the
in the general equation:
.
For the first line, and for the second
.
and so the lines are not perpendicular.
Example Question #2 : How To Find Out If Lines Are Perpendicular
Which of the following equations represents a line that is perpendicular to the line with points and
?
If lines are perpendicular, then their slopes will be negative reciprocals.
First, we need to find the slope of the given line.
Because we know that our given line's slope is , the slope of the line perpendicular to it must be
.
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