Question

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

Don't post useless ans.​

Answer 1

${\sf{\large{\bigstar{{ \underline{ \underline{ \: Given:}}}}}}}$

• Line AB
• A = (3,3)
• B = (-1,1)

${\sf{\large{\bigstar{{ \underline{ \underline{ \: \: To \: find :}}}}}}}$

• Slope of the line Perpendicular to line AB.

$\red{\sf{\large{\bigstar{{ \underline{ \underline{ \: Solution:}}}}}}}$

${ \sf{ We \: know \: that \: Slope \: of \: line \: joining \: two }} \\ {\sf{points \: is \: in \: form \: of (x_1,x_2) and (y_1,y_2)}}$

So, formula is,

${ \large{ \sf{ \boxed{ = \frac{y_2-y_1 }{x_2-x_1}}}}}$

Here,

${\sf{\implies{(x_1,y_1) = (3,3) }}}$

${\sf{\implies{(x_2,y_2) = (-1,1) }}}$

${\sf{\implies{(x_2,y_2) = (-1,1) }}}$

Slope of the line AB is ,

$\\ { \sf{ = \frac{1 - 3 }{ - 1 - 3}}}$

$\\ { \sf{ = \frac{ - 2 }{ - 4}}}$

$\\ { \sf{ = \frac{ \cancel 2 ^{1} }{ \cancel4 ^{2} }}}$

$\\ { \green{ \boxed{ \sf{ = \frac{ 1}{ 2 }}}}}$

So, Slope of the line Perpendicular to line AB is :-

Here m is 1/2.

${\large{ \sf{ \boxed{ = -\frac{1}{m}}}}}$

$\\ { \sf{ = - \frac{1}{ \frac{ 1}{2}}}}$

$\\ { \sf{ = -\frac{1×2}{1}}}$

$\\ { \color{green}{ \boxed{ \sf{ = -2}}}}$

Answer 2

Step-by-step explanation:

Given :

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

To Find :

• Find the slope of the line perpendicular

Solution :

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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