Calculate 8

Calculate the coordinates of point B axially symmetrical with point A[-1, -3] along a straight line p : x + y - 2 = 0.

Correct result:

x2 =  5
y2 =  3

Solution:

x1=1;y1=3 p:x+y2=0  qp;Aq q:xy+c=0    x1y1+c=0 (1)(3)+c=0  c=2  q:xy2=0  S=pq   x0+y02=0 x0y02=0  x0+y0=2 x0y0=2  x0=2 y0=0    x2=x1+2 x0=(1)+2 2=5
y2=y1+2 y0=(3)+2 0=3



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