Symmetry by plane

Determine the coordinates of an image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0

Correct answer:

x =  1
y =  -2
z =  2

Step-by-step explanation:

r:xy4z13=0 A(3,4,6)  n = s n = (1,1,4) p: x = t+a; y = t+b; z = 4t + c; t  R  3=t+a 4=t+b 6=4 t+c t=1  a+t=3 bt=4 c4t=6 t=1  t=11=1 c=6+4t=6+4 1=2 b=4+t=4+1=3 a=3t=31=2  a=2 b=3 c=2 t=1  p: x = t+2; y=t3; z = 4t2; t  R  p(t=1) = A  x=1+a=1+2=1
y=(1)+b=(1)+(3)=2
z=4 (1)+c=4 (1)+(2)=2



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