Question

Given a straight line `y=-1\2x+3` intersects the y-axis at point A and the x-axis at point B. A point P`(x.y)` divides the straight line in the ratio AB:BC = 1:2 .Find the coordinates of point P.?

Answer 1

Coordinates are `P(1/12,2)`

Explanation:

When a straight line `y=-12x+3` intersects `y`-axis at point A, coordinates of `A` are obtained by putting `x=0` i.e. `y=3` and coordinates are `A(0,3)` and for the `x`-axis at point B, put `y=0` which gives us `x=3/12=1/4` i.e. coordinates are `B(1/4,0)`.

Now coordinates of a point `P` which divides `A(x_1,y_1)` and `B(x_2,y_2)` in the ratio `l:m` are

`((lx_2+mx_1)/(l+m),(ly_2+my_1)/(l+m))`

Hence coordinates of point dividing `A(0,3)` and `B(1/4,0)` in the ratio `1:2` are

`((1xx1/4+2xx0)/3,(1xx0+2xx3)/3)` i.e. `P(1/12,2)`

graph{((x-1/12)^2+(y-2)^2-0.01)(x^2+(y-3)^2-0.01)((x-1/4)^2+y^2-0.01)(y+12x-3)=0 [-5.03, 4.97, -1.38, 3.62]}