Question

A line through point P(4,3) meets x-axis at A and y-axis at B.If BP is double of AP ,find the equation of line AB​

Answer 1

Given: A line through point P(4,3) meets x-axis at A and y-axis at B.

To find: The equation of line AB​.

Solution:

• We have provided that line through point P(4,3) meets x-axis at A and y-axis at B.

• Let A be (x,0) and B be (0,y).

• Now we have given that  BP is double of AP:

              BP/PA = 2/1

• P is dividing the line AB in ratio 2:1.

• So P will be:

              (mx2 + nx1) / m+n , (my2 + ny1) / m+n

              2x + 0 / 3 , 0 + y / 3

• Now comparing this with P(4,3), we get:

              2x/3 = 4, x = 6

              y/3 = 3, y = 9

• So A = (6,0) and B = (0,9)

• Now slope of line AB will be:

              9-0 / 0 - 6 = -3/2

• So equation of line AB will be:

              y - 0 = -3/2(x - 6)

              2y = -3x + 18

              3x + 2y = 18

Answer:

         The equation of line AB is 3x + 2y = 18