Question

Find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided by the xaxis . also find the coordinate of the point of division .

Answer 1

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Answer 2

Answer:

The x-axis divides the line segment AB in 1:1. The coordinates of the point of division are $(-\frac{3}{2},0)$.

Step-by-step explanation:

The coordinates of point A and B are A(1,-5) and B(-4,5).

Let the coordinates of the point of division are (x,0) and this point divides the line AB in k:1.

Using section formula,

$y=\frac{my_2+ny_1}{m+n}$

$0=\frac{k(5)+1(-5)}{k+1}$

$5k-5=0$

$5k=5$

$k=1$

Therefore the x-axis divides the line segment AB in 1:1.

Using section formula,

$x=\frac{mx_2+nx_1}{m+n}$

$x=\frac{1(-4)+1(1)}{1+1}$

$x=\frac{-4+1}{2}$

$x=\frac{-3}{2}$

Therefore the coordinates of the point of division are $(-\frac{3}{2},0)$.