Question

The vertices of a quadrilateral are $\mathrm{W}(1,2),\mathrm{X}(1,4),\mathrm{Y}(4,4)$ and $\mathrm{Z}(4,2)$. Draw the figure and its image after translation $3$ units left and $2$ units down.

Answer 1

Step 1: Find the coordinates of image after translation.

Given, coordinates are $\mathrm{W}(1,2),\mathrm{X}(1,4),\mathrm{Y}(4,4)$ and $\mathrm{Z}(4,2)$.

$\mathrm{a}=-2\mathrm{and}\mathrm{b}=-2$

Since, we know that to translate a figure $\text{'}\mathrm{a}\text{'}$ units horizontally and $\text{'}\mathrm{b}\text{'}$ units vertically in the coordinate plane. $\text{'}\mathrm{a}\text{'}$ is added to $\mathrm{x}-$coordinate and $\text{'}\mathrm{b}\text{'}$ is added to $\mathrm{y}-$coordinate of the vertices.

$\mathrm{A}(\mathrm{x},\mathrm{y})=\mathrm{A}\text{'}(\mathrm{x}+\mathrm{a},\mathrm{y}+\mathrm{b})$

The value of $\text{'}\mathrm{a}\text{'}$ and $\text{'}\mathrm{b}\text{'}$ will be positive if shift is right and vertically up and the value of $\text{'}\mathrm{a}\text{'}$ and $\text{'}\mathrm{b}\text{'}$ will be negative if shift is left and vertical down.

Using the above criteria of translation.

$$\begin{gathered} \mathrm{W}(1,2)=\mathrm{W}\text{'}(1-3,2-2)=\mathrm{W}\text{'}(-2,0) \\ \mathrm{X}(1,4),\mathrm{X}\text{'}(1-3,4-2)=\mathrm{X}\text{'}(-2,2) \\ \mathrm{Y}(4,4)=\mathrm{Y}\text{'}(4-3,4-2)=\mathrm{Y}\text{'}(1,2) \\ \mathrm{Z}(4,2)=\mathrm{Z}\text{'}(4-3,2-2)=\mathrm{Z}\text{'}(1,0) \end{gathered}$$

Step 2: Final answer.

Hence, the final coordinates after translation is $\mathrm{W}\text{'}(-2,0),\mathrm{X}\text{'}(-2,2),\mathrm{Y}\text{'}(1,2)\mathrm{and}\mathrm{Z}\text{'}(1,0)$.