question_answer

The ratio, in which the Y-axis divides the line segment joining the points (5, - 6) and (- 1, - 4) is

A) 1:5

B) 5:1

C) 2:4

D) None of these

Correct Answer: B

Solution :

Let AB be the given line segment with end points A(5, - 6) and B (- 1, - 4). Also, let y-axis divides AB in the ratio k: 1 at point P.

Then, by using section formula, Coordinates of

\[P=\left( \frac{-k+5}{k+1},\,\frac{-4k-6}{k+1} \right)\]     ...(1)

Since, on the Y-axis, abscissa is 0.

So, x-coordinate of P will be zero. On equating x-coordinate of P to 0, we get

\[\frac{-k+5}{k+1}=0\]

\[\Rightarrow \,\,\,-k+5=0\,\,\Rightarrow \,\,k=5\]

Thus, the required ratio is 5 : 1.