# Finding a point on the line joining two points in Cartesian coordinate system

Given a point A with coordinates (a,b) ; a point B with coordinates (c,d) , I want to find a point C's coordinate (x,y) ,with C lying on the line joining A and B and C is at a distance Dist from point A. This is the representation

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## 1 Answer

You will want to use Linear Interpolation. You can interpolate both the x and y coordinate independently. Let $\alpha = Dist/\sqrt{(c-a)^2+(d-b)^2}$. Then the interpolated point is given by:

$$x = a + \alpha(c-a)$$

and

$$y = b + \alpha(d-b)$$

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