Question

Draw the figure and its reflection in

1. the $\mathrm{x}-$axis and
2. the $\mathrm{y}-$axis

Identify the coordinates of the image.

Given, $\mathrm{D}(-5,-5),\mathrm{E}(-5,0),\mathrm{F}(-2,-2),\mathrm{G}(-2,-5)$

Answer 1

Step 1: Find the coordinates of image after reflection in $\mathrm{x}-$axis.

Given, coordinates are $\mathrm{D}(-5,-5),\mathrm{E}(-5,0),\mathrm{F}(-2,-2),\mathrm{G}(-2,-5)$

As we know reflection about the $\mathrm{x}-$axis, then coordinates changes as:

$\mathrm{A}(\mathrm{x},\mathrm{y})=\mathrm{A}\text{'}(\mathrm{x},-\mathrm{y})$

Using the above criteria for reflection in the $\mathrm{x}-$axis.

$$\begin{gathered} \mathrm{D}(-5,-5)=\mathrm{D}\text{'}(-5,5) \\ \mathrm{E}(-5,0)=\mathrm{E}\text{'}(-5,0) \\ \mathrm{F}(-2,-2)=\mathrm{F}\text{'}(-2,2) \\ \mathrm{G}(-2,-5)=\mathrm{G}\text{'}(-2,5) \end{gathered}$$

Step 2: Draw the figure of image after refection in $\mathrm{x}-$axis.

Step 3: Find the coordinates of image after reflection in $\mathrm{y}-$axis.

As we know reflection about the $\mathrm{y}-$axis, then coordinates changes as:

$\mathrm{A}(\mathrm{x},\mathrm{y})=\mathrm{A}\text{'}(-\mathrm{x},\mathrm{y})$

Using the above criteria for reflection in the $\mathrm{y}-$axis.

$$\begin{gathered} \mathrm{D}(-5,-5)=\mathrm{D}\text{'}(5,-5) \\ \mathrm{E}(-5,0)=\mathrm{E}\text{'}(5,0) \\ \mathrm{F}(-2,-2)=\mathrm{F}\text{'}(2,-2) \\ \mathrm{G}(-2,-5)=\mathrm{G}\text{'}(2,-5) \end{gathered}$$

Step 4: Draw the figure of image after refection in $\mathrm{y}-$axis.

Step 5: Final answer.

Hence, the coordinates of image after reflection in the $\mathrm{x}-$axis and $\mathrm{y}-$axis are $\mathrm{D}\text{'}(-5,5),\mathrm{E}\text{'}(-5,0),\mathrm{F}\text{'}(-2,2),\mathrm{G}\text{'}(-2,5)$ and $\mathrm{D}\text{'}(5,-5),\mathrm{E}\text{'}(5,0),\mathrm{F}\text{'}(2,-2),\mathrm{G}\text{'}(2,-5)$.