Question

Find the slope of the line perpendicular to the line AB, if A is (3, 3) and B is (-1, 1)​

Answer 1

SOLUTION

TO DETERMINE

The slope of the line perpendicular to the line AB, if A is (3, 3) and B is (-1, 1)

EVALUATION

Here the coordinates of the given two points A & B are

( 3 , 3 ) & ( -1 , 1 ) respectively

So the slope of the line AB joining the points A and B is

$\displaystyle \sf{m = \frac{3 - 1}{3 + 1} }$

$\implies \displaystyle \sf{m = \frac{2}{4} }$

$\implies \displaystyle \sf{m = \frac{1}{2} }$

Let M be the the slope of the line perpendicular to the line AB

Then by the condition of perpendicularity

$\displaystyle \sf{m \times M= - 1 }$

$\implies \displaystyle \sf{M= - \frac{1}{m} }$

$\implies \displaystyle \sf{M= - 2 }$

FINAL ANSWER

The slope of the line perpendicular to the line AB, if A is (3, 3) and B is (-1, 1) is - 2

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