What is the slope of any line perpendicular to the line passing through #(-9,8)# and #(3,-3)#?

1 Answer
Feb 7, 2016

Answer:

12/11

Explanation:

The coordinates given can be used to determine the gradient.

In standard form the equation of a straight line is:

#" "y=mx+c#

Where #m# is the gradient (slope)

The trick is, that the gradient of the line perpendicular to the first is:

#" "-1/m#
So all you need to do is find the gradient of the first line then the other is just a matter of turning the first one 'upside down' and multiplying it by (-1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let #(x_1,y_1) -> (-9,8)#
Let #(x_2,y_2)->(3,-3)#

Then the gradient is:

# m" "=" "(y_2-y_1)/(x_2-x_1)#

#=""(-3-8)/(3-(-9))#

#=""(-11)/(+12)#

#=-11/12#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So for the perpendicular line its gradient is:

#(-1)xx1/m" " ->" " (-1)xx(-12/11) =+12/11#