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

Answer:

The coordinates of D' and F are;

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

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;

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