Question

A translation maps ADEF onto AD'E'F'. Use the coordinates D(5, 2), E(7, -3), E'(2-6), and F'(4, 7) to determine the coordinates of D' and F.

Answer 1

The coordinates of D' and F are;

`\begin{gathered} D^(\prime)(0,-1) \\ F(9,10) \end{gathered}`

Step-by-step explanation:

Given the triangles DEF mapped onto D'E'F'.

Given then the coordinate;

`\begin{gathered} D(5,2) \\ E(7,-3) \\ E^(\prime)(2,-6) \\ F^(\prime)(4,7) \end{gathered}`

Let us find the translation used to map triangle DEF to D'E'F'.

`\begin{gathered} E(7,-3)\rightarrow E^(\prime)(2,-6) \\ (x,y)\rightarrow(x+(2-7),y+(-6--3)) \\ (x,y)\rightarrow(x-5,y-3) \end{gathered}`

Applying the translation to point D;

`\begin{gathered} (x,y)\rightarrow(x-5,y-3) \\ D(5,2)\rightarrow D^(\prime)(5-5,2-3) \\ D(5,2)\rightarrow D^(\prime)(0,-1) \end{gathered}`

Also to get F;

`\begin{gathered} F(x,y)\rightarrow F^(\prime)(x-5,y-3) \\ F^(\prime)(4,7) \\ x-5=4 \\ x=4+5 \\ x=9 \\ y-3=7 \\ y=7+3 \\ y=10 \\ \end{gathered}`

The coordinate of point F is;

`F(9,10)`

Therefore, the coordinates of D' and F are;

`\begin{gathered} D^(\prime)(0,-1) \\ F(9,10) \end{gathered}`