Question

The vertices of a triangle are $\mathrm{A}(-4,2),\mathrm{B}(-2,2)$ and $\mathrm{C}(-3,4)$. Rotate the triangle as described. Find the coordinates of the image.

$270°$ clockwise about the origin.

Answer 1

Find the coordinates of image after rotation.

Given, coordinates are $\mathrm{A}(-4,2),\mathrm{B}(-2,2)$ and $\mathrm{C}(-3,4)$.

Since, we know that rotation of $270°$ clockwise about the origin then coordinates changes as:

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

Using the above criteria of rotation of $270°$ clockwise about the origin.

New coordinates will be,

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

Hence, the coordinates of image after rotation are $\mathrm{A}\text{'}(-2,-4),\mathrm{B}\text{'}(-2,-2)$ and $\mathrm{C}\text{'}(-4,-3)$.