Question

the coordinates of DEFG are D(2,-1), E(5,-2) F(4,-5), and G(1,-4). Describe in coordinate mapping notation a translation that will move vertex E to the origin.

Answer 1

A translation is given as:

$(x,y)\rightarrow(x+a,y+b)$

We need to find the translation that takes E to the origin that is:

$(5,-2)\rightarrow(5+a,-2+b)=(0,0)$

Then we have the equations:

$\begin{gathered} 5+a=0 \\ a=-5 \end{gathered}$

and

$\begin{gathered} -2+b=0 \\ b=2 \end{gathered}$

Therefore the translation is:

$(x,y)\rightarrow(x-5,y+2)$