Answer :

Given: line segment A ( -2,5) and B(3, -5)

To find: the coordinates of the point P which divides the line segment AB into the ratio 2:3

Explanation: Given P divides the line segment AB into 2:3 ratio, let point P be denoted as P(x,y)

So, applying the section formula, we get

In this case, m_{1} = 2, m_{2} = 3

And x_{1} = - 2, x_{2} = 3, y_{1} = 5 and y_{2} = - 5

Substituting the above values in section formula, we get

Hence the P (0, 1)

So, the coordinates of the point P which divides the line segment AB into the ratio 2:3 are 0 and 1.

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