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.  q⊥p;A∈q  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)=q∩p  −x+2⋅ y+7=0 2⋅ x+y+1=0  x−2y=7 2x+y=−1  x=1 y=−3  d=(Bx−x)2+(By−y)2=(1−1)2+((−3)−(−3))2=0

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