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Whether the end-point is x% closer to an arbitrary point when compared to the start-point

I am having three coordinate locations A(x1, y1), B(x2, y2) and C(x3, y3). A is the starting location, B is the end location and C is the arbitrary coordinate location. Now I want to calculate whether the end-location(B) at least 25% closer to the point-location(C) when compared to start-location(A).

Can someone write pseudocode for this problem?

Solution

  • This is simple vector geometry:

    The squared distance d2 from A to B is (Ax - Bx)^2 + (Ay - By)^2

    So B to C is 25% less than A to C if:

    sqrt(d2(A,C)) * 0.75 >= sqrt(d2(B,C))

    And simplified, so you dont need to deal with roots:

    d2(A, C) * 0.75^2 >= d2(B, C)