Question

answer all parts of the question on the graph to the right. plot the pre - image and label it appropriately. make sure to show the transformations using different colors and labeling them appropriately. show the line of reflection when reflecting.
. plot the pre - image, pentagon jklmn: j(2,4), k(3,7), l(4,5), m(5,7), n(6,4).
. then, translate the pentagon (x,y)→(x - 4,y - 2) creating image jklmn.
. then, reflect jklmn across the line y = x to create image jklmn

Explanation:

Step1: Plot pre - image points

Plot points J(2, 4), K(3, 7), L(4, 5), M(5, 7), N(6, 4) on the coordinate plane and label the pentagon as JKLMN.

Step2: Apply translation

For point J(2, 4), using the translation rule $(x,y)\to(x - 4,y - 2)$, we have $J'(2-4,4 - 2)=J'(-2,2)$.
For point K(3, 7), $K'(3-4,7 - 2)=K'(-1,5)$.
For point L(4, 5), $L'(4-4,5 - 2)=L'(0,3)$.
For point M(5, 7), $M'(5-4,7 - 2)=M'(1,5)$.
For point N(6, 4), $N'(6-4,4 - 2)=N'(2,2)$. Plot and label pentagon J'K'L'M'N'.

Step3: Apply reflection across $y = x$

The rule for reflecting a point $(x,y)$ across the line $y = x$ is $(x,y)\to(y,x)$.
For J'(-2,2), $J''(2,-2)$.
For K'(-1,5), $K''(5,-1)$.
For L'(0,3), $L''(3,0)$.
For M'(1,5), $M''(5,1)$.
For N'(2,2), $N''(2,2)$. Plot and label pentagon J''K''L''M''N'' and draw the line $y = x$ as the line of reflection.

Answer:

Pre - image points J(2, 4), K(3, 7), L(4, 5), M(5, 7), N(6, 4) are plotted. Translated points J'(-2,2), K'(-1,5), L'(0,3), M'(1,5), N'(2,2) are plotted and then reflected points J''(2,-2), K''(5,-1), L''(3,0), M''(5,1), N''(2,2) are plotted with line $y = x$ as the line of reflection.