\[(x_2-x_1)^2 + (y_2-y_1)^2 = (x_2-x_1)^2(cos^2x+sin^2x) + (y_2-y_1)^2(cos^2x+sin^2x)\]
\[= [(x_2-x_1)^2cos^2x - 2cosxsinx(x_2-x_1)(y_2+y_1)+(y_2+y_1)^2sin^2x] + [(x_2-x_1)^2sin^2x+2cosxsinx(x_2-x_1)(y_2+y_1)+(y_2+y_1)^2cos^2x]\]
\[= [(x_2-x_1)cosx - (y_2+y_1)sinx]^2 [(x_2-x_1]sinx+(y_2-y_1)cosx]^2\]