# What are the coordinates of A if P is in the middle of the line AB such that B(2,-3) and P(-3,5).

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The point between the points (x1, y1) and ( x2, y2) has the coordinates [(x1+x2)/2 , (y1+y2)/2]

Here, we are given the points B(2,3) and P(-3, 5). P lies between A and B and we have to determine the co-ordinates of A. Let the co-ordinates of A be (x , y)

So we have -3 = (2 + x)/2

=> -6 = 2 + x

=> x = -8

5 = (-3 + y)/2

=> -3 + y = 10

=> y = 13

**The required coordinates of A are (-8, 13)**

Given the line segment AB such that B(2, -3)

Also, given the point P(-3,5) is midpoint of AB.

Then we will use the midpoint formula to find the coordinates of A.

We know that:

Px = (Ax+ Bx)/2

==> -3 = (Ax + 2) /2

==> Ax + 2 = -6

==> Ax = -8..............(1)

Also, we know that:

Py = (Ay+By)/2

==> 5 = (Ay + -3) /2

==> Ay -3 = 10

==> Ay = 13..............(2)

**Then the coordinates of the point A is ( -8. 13).**