Question

Find the slope of any line perpendicular to the line through (5,3) and (2,5)

Answer 1

For this case we have that the slope of a line is given by:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

Where:

$(x_ {1}, y_ {1})$ and$(x_ {2}, y_ {2})$ are two points through which the line passes.

According to the statement we have to:

$(x_ {1}, y_ {1}) :( 2,5)\\(x_ {2}, y_ {2}): (5,3)$

Then, the slope of the line is:

$m = \frac {3-5} {5-2} = \frac {-2} {3} = - \frac {2} {3}$

By definition, if two lines are perpendicular then the product of their slopes is -1, that is:

$m_ {1} * m_ {2} = - 1$

We find $m_ {2}:$

$m_ {2} = \frac {-1} {- \frac {2} {3}}\\m_ {2} = \frac {3} {2}$

Answer:

The slope of a perpendicular line is:

$m_ {2} = \frac {3} {2}$