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.?

1 Answer
Shwetank Mauria
Apr 23, 2018

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]}

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