The mirror image of the point (1,2,3) in a plane is (-73,-43,-13).

Question

The mirror image of the point $(1,2,3)$ in a plane is $\left(-\dfrac73,-\dfrac43,-\dfrac13\right)$. Which of the following points lies on this plane?

Accepted Answer

Normal direction $=\left(-	frac73-1,-	frac43-2,-	frac13-3ight)=\left(-	frac{10}3,-	frac{10}3,-	frac{10}3ight)\parallel(1,1,1)$.
Midpoint $=\left(\dfrac{1-\frac73}{2},\dfrac{2-\frac43}{2},\dfrac{3-\frac13}{2}ight)=\left(-	frac23,	frac13,	frac43ight)$.
Plane: $\left(x+	frac23ight)+\left(y-	frac13ight)+\left(z-	frac43ight)=0\implies x+y+z=1$.
Testing options: only $B(1,-1,1)$ gives $1-1+1=1$ .

Solutions · 1