Question

Find the ratio in which the line segment joining the points (-3, 8) and (5, - 9) is divided by (0, 2).

• A. 3:5
• B. 6:11
• C. Both A and B
• D. The case is not possible

Answer 1

The correct option is D

The case is not possible

Let the ratio in which the line segment joining (-3, 8) and (5, - 9) is divided by (0, 2) be k : 1.
Therefore, $0=\frac{5k-3}{k+1}$
$5k-3=0$
$k=\frac{3}{5}$
Therefore, the required ratio is 3:5.
This was obtained using the x-coordinate as the reference.

If we now use the y-coordinate, we have
$2=\frac{-9k+8}{k+1}$
$2k+2=-9k+8$
$11k=6$
$k=\frac{6}{11}$

Now we get two different ratios, one when we use the formula for x-coordinate, and the other when we use the formula for the y-coordinate.

This means that the points in question are not collinear.

Hence, the point (0, 2) cannot divide the join of (-3, 8) and (5, - 9).