In what ratio does the point (-2,-5) divide the segment AB where A is

When we plot the points provided on the XY-plane, we see that A(2,3) is in the first quadrant and B(-1,-3) is in the third quadrant.

Let us connect A and B using a straight line. Let us name the point (-2,-5) as C.
Clearly, C is not in between A and B on the line connecting A and B. Hence, we can say that it does not divide the line connecting A and B internally. Hence, options B and D can be ruled out.

Now, using the distance formula, we can find that AB = 3√5 and AC = 4√5. Therefore, BC = √5.

Clearly, the ratio of AC to BC is 4:1 and the point is external to the points A and B. Therefore, option C has to be the answer.

Point to note - There is no need to remember complex formulae (Section formulae) to be able to tackle such questions. A smart approach is to eliminate options based on the position of the dividing point with respect to the endpoints. Post this, usage of the distance formula will help us determine the ratio of the line segments.

Cheers,
Crackverbal Academics Team