What is the slope of any line perpendicular to the line passing through #(2,2)# and #(9,5)#?

2 Answers
Feb 27, 2016

Answer:

#-7/3#

Explanation:

the slope of the line passing through the given pts is #(5-2)/(9-2)=3/7#
negative inverse of this slope will be the slope of the line perpendicular to the line joining the given pts.
Hence the slope is #-7/3#

Feb 27, 2016

Answer:

The gradient of the perpendicular line is#" " -7/3#

Explanation:

The standard form equation for a straight line graph is:

#" "y=mx+c#

Where

#x# is the independent variable (may take on any value you wish)

#y# is the dependant variable (its value deponds an what value you give #x#)

#c# is a constant

#m# is the gradient (slope)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the gradient of the given line")#

Let #(x_1,y_1) -> (2,2)#
Let #(x_2,y_2)-> (9,5)#

Then it follows that

#m" "=" " (y_2-y_1)/(x_2-x_1) = (5-2)/(9-2) = 3/7#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the slope of any line perpendicular to this")#

Given that the first line had gradient #m=3/7#

and that the gradient of the perpendicular line is #(-1)xx 1/m#

Then we have: # (-1)xx7/3=-7/3#