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 $5\mathrm{unit}$ right.

Answer 1

We know that to translate a figure ‘a’ units horizontally and ‘b’ units vertically in the coordinate plane, $\mathrm{a}$ is to be added to the
x-coordinate and $\mathrm{b}$ is to be added to the y-coordinates of the vertices. Then new coordinates become:-
$\mathrm{A}(\mathrm{x},\mathrm{y})\to \mathrm{A}\text{'}(\mathrm{x}+\mathrm{a},\mathrm{y}+\mathrm{b})$
The value $‘\mathrm{a}’\mathrm{and}‘\mathrm{b}’$ will be positive if the shift is Right and Vertical up respectively and the value of $‘\mathrm{a}’\mathrm{and}‘\mathrm{b}’$ will be negative if the shift is left and vertical down respectively.
Now we have given:-
$\mathrm{L}(0,1),\mathrm{M}(1,-2),\mathrm{N}(-2,1)\mathrm{and}\mathrm{a}=5,\mathrm{b}=0$

$\mathrm{L}\text{'}(0+\mathrm{a},1+\mathrm{b})=\mathrm{L}\text{'}(0+5,1+0)=\mathrm{L}\text{'}(5,1)$

$\mathrm{M}\text{'}(1+\mathrm{a},-2+\mathrm{b})=\mathrm{M}\text{'}(1+5,-2+0)=\mathrm{M}\text{'}(6,-2)$

$\mathrm{N}\text{'}(-2+\mathrm{a},1+\mathrm{b})=\mathrm{N}\text{'}(-2+5,1+0)=\mathrm{N}\text{'}(3,1)$

Hence, the coordinate of image after the translation $5\mathrm{unit}$ right are $\mathrm{L}\text{'}(5,1),\mathrm{M}\text{'}(6,-2),\mathrm{N}\text{'}(3,1)$

Final Answer: The coordinate of image are $\mathrm{L}\text{'}(5,1),\mathrm{M}\text{'}(6,-2),\mathrm{N}\text{'}(3,1)$