Question

In what ratio is the line joining A(0, 3) and B(4,-1) divided by the x-axis? Write the coordinates of the point where AB intersects the x-axis.

Answer 1

Let the line segment AB intersects the x-axis by point P (x, 0) in the ratio k: 1.

$(x,0)=(\frac{k\times 4+1\times 0}{k+1},\frac{k\times (-1)+1\times 3}{k+1})(x,0)=(\frac{4k}{k+1},\frac{-k+3}{k+1})0=\frac{-k+3}{k+1}k=3\text{Thus the required ratio in which P divides AB is 3:1}\text{Also, we have:}x=\frac{4k}{k+1}\Rightarrow x=\frac{4\times 3}{3+1}=\frac{12}{4}=3\text{Thus the coordinates of the point P is (3,0)}$