Question

The vertices of a triangle are $\mathrm{L}(0,1),\mathrm{M}(1,-2)$ and $\mathrm{N}(-2,1)$. Draw the figure and its image after the translation $(\mathrm{x}+2,\mathrm{y}+3)$.

Answer 1

Step 1: Find the new coordinates after translation.

Given coordinates are $\mathrm{L}(0,1),\mathrm{M}(1,-2)$ and $\mathrm{N}(-2,1)$.

We know that to translate a figure $\text{'}\mathrm{a}\text{'}$ units horizontally and $\text{'}\mathrm{b}\text{'}$ units vertically in the coordinates plane, $\text{'}\mathrm{a}\text{'}$ is added to the $\mathrm{x}-$ coordinate and $\text{'}\mathrm{b}\text{'}$ is to be added to the $\mathrm{y}-$ coordinates of the vertices. Then, new coordinate will be,

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

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

Now, we have given $\mathrm{L}(0,1),\mathrm{M}(1,-2),\mathrm{N}(-2,1)$ and $(\mathrm{x}+2,\mathrm{y}+3)$

From this we get value of $\mathrm{a}=2,\mathrm{b}=3$

So, the new coordinates will be,

$$\begin{gathered} \Rightarrow \mathrm{L}(0,1)=\mathrm{L}\text{'}(0+2,1+3)=\mathrm{L}\text{'}(2,4) \\ \Rightarrow \mathrm{M}(1,-2)=\mathrm{M}\text{'}(1+2,-2+3)=\mathrm{M}\text{'}(3,1) \\ \Rightarrow \mathrm{N}(-2,1)=\mathrm{N}\text{'}(-2+2,1+3)=\mathrm{N}\text{'}(0,4) \end{gathered}$$

Step 2: Draw the figure.

Hence, the required figure for coordinates $\mathrm{L}\text{'}(2,4),\mathrm{M}\text{'}(3,1)$ and $\mathrm{N}\text{'}(0,4)$ is drawn above.