Question

The line joining the points A(-2, 1) and B(3, 4) is divided by the x-axis. Find the point of division?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

By marking the points on the coordinate system we can see that x-axis cuts the line joining the points A and B externally and y-axis cuts the line internally

AB cuts the x-axis at P and y-axis at Q.

Suppose, P divides AB externally in the ratio k:1

P(x,y) = $(\frac{k.3-(-1)(-2)}{k-1},\frac{k\times 4-1\times 1}{k-1})$

= $(\frac{3k+2}{k-1},\frac{4k-1}{k-1})$

But this is the point om x-axis. Y coordinate = 0

$\frac{4k-1}{k-1}=0$

$k=\frac{1}{4}$

The point of division on x - axis

= $(\frac{3\times \frac{1}{4}+2}{\frac{1}{4}-1},\frac{4\times \frac{1}{4}-1}{\frac{1}{4}-1})$

p(x,y) = $(\frac{-11}{3},0)$