Question

Find the ratio in which the line segment joining A(1, -5) B(-4, 5) is divided by the x-axis

• A. 1:2
• B. 1:1
• C. 2:1
• D. 1:4

Answer 1

The correct option is B

1:1

After plotting the points, we can see that x-axis cuts the line joining the points A and B internally.

Let x-axis cut the line at p in the ratio k: 1.

Point p $\{\frac{k(-4)+1.\left(1\right)}{k+1},\frac{k\left(5\right)+1(-5)}{k+1}\}$

p$(\frac{-4k+1}{k+1},\frac{5k-5}{k+1})$

This coordinate lies on the x-axis

y=0

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

k = 1

So, x-axis cuts the line in the ratio

1:1