# How to solve this kind of questions translation of $3D$

Translate $\Delta PQR$ with vertices $P(2, 4, -7), Q(3, 7, 18), R(-5, 12, 8)$ by $(-3, 2, 5)$. This is my question , it came in our test and I am afraid to come in the final exam so kindly, I want to know how to solve such questions, our lecturer tough us only about $2D$ and he did not teach us about $3D$ so I understand $2D$ but I could not understand $3D$ . Please, can you explain the solution step by step because I want to know how you solve it?

Just add the corresponding coordinates. So $P$ becomes $(2,4,-7)+(-3,2,5) = (2+(-3),4+2,-7+5) = (-1,6,-2)$. Repeat for $Q,R$. – copper.hat Nov 2 '12 at 14:55
Denote by $\tau(PQR)=\tau P \tau Q \tau R$ translated triangle from conditions we have that $$\tau P=\tau(2,4,-7)=(2,4,-7)+(-3,2,5)=(2-3,4+2,-7+5)=(-1,6,-2)$$ $$\tau P=\tau(3,7,18)=(3,7,18)+(-3,2,5)=(3-3,7+2,18+5)=(0,9,33)$$ $$\tau P=\tau(-5,12,8)=(-5,12,8)+(-3,2,5)=(-5-3,12+2,8+5)=(-8,14,13)$$
$$\tau(PQR=(-1,6,-2),(0,9,33),(-8,14,13)$$