Question

The vertices of a triangle are $\mathrm{A}(2,5),\mathrm{B}(1,2)$ and $\mathrm{C}(3,1)$. Find the coordinates of the image after the transformations given.

Rotate $90°$ clockwise about the origin.

Answer 1

Find the coordinates of image after rotation.

Given, coordinates are $\mathrm{A}(2,5),\mathrm{B}(1,2)$ and $\mathrm{C}(3,1)$.

Since, we know that rotation $90°$ clockwise about the origin then the coordinates changes as:

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

Using the above criteria of rotation of $90°$ clockwise about the origin,

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

Hence, the coordinates of image after rotation are $\mathrm{A}\text{'}(2,-5),\mathrm{B}\text{'}(1,-2),\mathrm{C}\text{'}(3,-1)$.