Question

Determine the ratio in which the line 2x + y - 4 = 20 divide the line segment joining the points a bracket 2, - 2 and b 3, 7

Answer 1

By the two point form, we have to find the equation of the line passing through A and B.

y+2=((7+2)/(3-2))*(x-2)

Or

y+2=9x - 18

Or

y=9x-20

Given, equation of another line:

2x+y-4=20

Or

y=-2x-24

since the point of intersection lies on both the lines so, in the two equations value of x and y would be equal

solving simultaneous equations, we get

x=4, y=16

so, the point of intersection would be (4,16)

by observing the coordinates, we can obtain that this is an external division

now by using section formula

(4,16)=((3m-2n)/(m-n), (7m-2n)/(m-n))

so on comparing LHS and RHS we get

4(m-n)=3m-2n

Or 4m-4n=3m-2n

Or m=2n

so the simplest ratio between m and n =m:n

=2n:n

=2:1