What is the answer to this question.

I don't think I have ever seen a question worded with "partitions AB in the ratio".

But if it means what I think it means, a figure could explain it better.

o Here is B(2,0)

o Here is P(-1,-2.4)

Here is A(-3,-4)o

There is a straight line from the bottom point (A) to the top point (B) and its equation is y=0.8x-1.6

The point (-1, -2.4) lies on the line from A to B, but not in the center.

If you find the distance from A to P, then find the distance from P to B, you can make a ratio of the two lengths.

AP = sqrt[(-1-(-3))2+(-2.4-(-4))2] = sqrt[22+1.62] = sqrt[6.56] = 2.561
PB = sqrt[(-1-2)2+(-2.4-0)2]=sqrt[(-3)2+(-2.4)2] = sqrt[14.76] = 3.842

So the two parts are in the ratio 2.561 : 3.842 (AP : PB) or 2.561/3.842 = 0.66658 = 2/3 (approx)

The point P partitions AB into two segments with ratio 2/3

Not sure if that what you mean because there isn’t a lot of context but hope that helped, have a great day