Question

Find the coordinates of foot of perpendicular from the point p (1, 2) in the line x-3y + 4 = 0.

Answer 1

Please see the attachment

Answer 2

Given :  perpendicular from (1, 2) to the line x - 3y + 4 = 0.

To Find :  foot of the perpendicular from (1, 2) to the line x - 3y + 4 = 0

Solution:

x - 3y + 4 = 0

=> 3y = x + 4

=> y = x/3 + 4/3

Slope = 1/3

Slope of perpendicular line = - 3

passes through ( 1 , 2)

y - 2 =(-3)(x - 1)

=> y -2 = -3x + 3

=> 3x + y = 5

3y = x + 4

3x + y = 5 => 9x + 3y = 15

=> 9x + x + 4 = 15

=> 10x = 11

=> x = 11/10

3x + y = 5

=> y = 5 - 3(11/10)

=> y = 17/10

(11/10) , ( 17/10)

(1 .1 , 1.7) is foot of the perpendicular from (1, 2) to the line x - 3y + 4 = 0.

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