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

Answer 1

#-7/3#

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#

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Answer 2

Eli Assouline

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

An equation in standard form for a graph with a straight line 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)#

Consequently, 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#

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Answer 3

Eva Adamson

The slope of any line perpendicular to the line passing through (2,2) and (9,5) is -3/7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.