Find point p that divides segment ab into a 2: 3 ratio. the point should be closer to a. a(-3,1) and b(3,5)

First, work out how much you need to add to A's x and y coordinates in order to get to point B from point A.

So (using Ax to mean x-coordinate of A, Ay the y-coordinate of A, etc):
x-difference = Bx - Ax = 3 - (-3) = 3 + 3 = 6
y-difference = By - Ay = 5 - 1 = 4

Now, if the point divides the segment AB in the ratio 2:3, then it is 2/(2+3) of the way along the line AB.

i.e. it is 2/5 of the way along the line AB.

We therefore need to add 2/5 of the x- and y-differences to point A to get point p:
px = Ax + (2/5)*(x-difference) = -3 + (2/5)*6 = -3 + 12/5 = -15/5 + 12/5 = -3/5 = -0.6
py = Ay + (2/5)*(y-difference) = 1 + (2/5)*4 = 1 + 8/5 = 5/5 + 8/5 = 13/5 = 2.6

Therefore coordinates of p are (-0.6, 2.6)

Im sorry but what on

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