Perpendicular projection

Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0.

Correct result:

d =  0

Solution:

Bx=1;By=3 Ax=3;Ay=2  p:2 x+y+1=0.  qp;Aq  q:x+2y+c=0    Ax+2 Ay+c=0 3+2 (2)+c=0  c=7  q:x+2y+7=0  X=(x,y)=qp  x+2 y+7=0 2 x+y+1=0  x2y=7 2x+y=1  x=1 y=3  d=(Bxx)2+(Byy)2=(11)2+((3)(3))2=0



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