Question

find the value of p when the line through the points (2,2) and (5,7) is perpendicular to the line 3x+py-9=0.

Answer 1

Hi ,

i ) Slope ( m ) of a line passing through

the points A( x1 , y1 ) = ( 2 , 2 ) and

B( x2 , y2 ) = ( 5 , 7 ) is

m1 = ( y2 - y1 )/( x2 - x1 )

m1 = ( 7 - 2 )/( 5 - 2 )

m1 = 5/3 ----( 1 )

ii ) slope of a line perpendicular to AB

line ( m2 ) = - 3/5 ----( 2 )

iii ) Slope of a line 3x + py - 9 = 0

slope = - 3/p ---( 3 )

( 2 ) and ( 3 ) shows slope of a same line.

( 2 ) = ( 3 )

- 3/5 = - 3/p

p = 5

I hope this helps you.

: )

Answer 2

A(2,2) and B(5,7) are the given points.

We know that the slope of the line through the points (x1,x2)and(y1,y2) is y2-y1 / x2-x1

Then the slope of the line AB is m1 = 7-2 / 5-2 = 5/3.

The given eqn of the other line is: 3x + Py - 9 = 0 ---(1)

We know that the slope of the line ax+by+c=0 is "-co-efficient of x / co-efficient of y".

then the slope of the line 3x + Py - 9 = 0 is m2 = -3/P.

For two lines to be perpendicular, the product of their slopes should be -1.

i.e., m1.m2 = -1

5/3 x -3/P = -1.

-5/P = -1

P = 5

Answer to this question is 5.