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.

$\mathrm{A}(2,0),\mathrm{B}(1,5),\mathrm{C}(4,3)$

Answer 1

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

Given, coordinates $\mathrm{A}(2,0),\mathrm{B}(1,5),\mathrm{C}(4,3)$

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

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

Reflection in the $\mathrm{x}-$axis:

$$\begin{gathered} \mathrm{A}(2,0)=\mathrm{A}\text{'}(2,0) \\ \mathrm{B}(1,5)=\mathrm{B}\text{'}(1,-5) \\ \mathrm{C}(4,3)=\mathrm{C}\text{'}(4,-3) \end{gathered}$$

Step 2: Draw the figure for reflection in the $\mathrm{x}-$axis.

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

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

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

Reflection in the $\mathrm{x}-$axis:

$$\begin{gathered} \mathrm{A}(2,0)=\mathrm{A}\text{'}(-2,0) \\ \mathrm{B}(1,5)=\mathrm{B}\text{'}(-1,5) \\ \mathrm{C}(4,3)=\mathrm{C}\text{'}(-4,3) \end{gathered}$$

Step 4: Draw the figure for reflection in the $\mathrm{y}-$axis.

Step 5: Final answer.

Hence, the coordinates after reflection in the $\mathrm{x}-$axis and for $\mathrm{y}-$axis are $\mathrm{A}\text{'}(2,0),\mathrm{B}\text{'}(1,-5),\mathrm{C}\text{'}(4,-3)$ and $\mathrm{A}\text{'}(-2,0),\mathrm{B}\text{'}(-1,5),\mathrm{C}\text{'}(-4,3)$.