Question

Determine the ratio in which the line 2x+y=4 divides the line segment joining the points A(2,-2) and B(3,7)

Answer 1

The line is 2x+y=4

Given points are (2,-2) and (3,7)

Let the ratio be k:1

The coordinates of point P is
[ k(3)+1(2)/k+1,k(7)+1(-2)/k+1]
(Section formula)

=(3k+2)/k+1,(7k-2)/k+1

Since this point P lies on the line. Substitute P in 2x+y=4

2((3k+2)/(k+1))+(7k-2)/(k+1)

We get K =2/9
Ratio is 2:9