Question

A translation maps ABC onto A'B'C'. Use the coordinates A(-3, 0), B(4, 2), B'(0, 0), and C'(6, 3) to determine the translation vector and thecoordinates of C.

Answer 1

Given that a translation maps triangle ABC onto A'B'C'.

with coordinates;

`\begin{gathered} A(-3,0) \\ B(4,2) \\ B^(\prime)(0,0) \\ C^(\prime)(6,3) \end{gathered}`

Let us find the translation vector;

`\begin{gathered} B(4,2)\rightarrow B^(\prime)(0,0) \\ \\ <0-4,0-2> \\ <-4,-2> \end{gathered}`

Therefore, the translation vector is;

`<-4,-2>`

Solving for point C;

`\begin{gathered} C(x,y)\rightarrow C^(\prime)(x-4,y-2)=C^(\prime)(6,3) \\ \\ x-4=6 \\ x=6+4 \\ x=10 \\ y-2=3 \\ y=3+2 \\ y=5 \\ C(10,5) \end{gathered}`

Therefore, the coordinate of C is;