find the point new position

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$P_2(x=x_1+rcosθ,y=y_1+rsinθ)$ , where $r=d(P_1,P_2)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

You can easily calculate $θ$ from the triangle $P_1P_3P_4$ and substitute it. This is if the line $P_1P_2$ is parallel to your horizontal axis, if not then you should find the angle between them also