Question

A triangle is graphed in the coordinate plane. What are the coordinates of the image after a translation $3$ unit's right and $2$ unit's down?

• A. $\mathrm{A}\text{'}(1,4),\mathrm{B}\text{'}(1,1),\mathrm{C}\text{'}(3,1)$
• B. $\mathrm{A}\text{'}(1,2),\mathrm{B}\text{'}(1,-1),\mathrm{C}\text{'}(3,-1)$
• C. $\mathrm{A}\text{'}(-2,2),\mathrm{B}\text{'}(-2,-1),\mathrm{C}\text{'}(0,-1)$
• D. $\mathrm{A}\text{'}(0,1),\mathrm{B}\text{'}(0,-2),\mathrm{C}\text{'}(2,-2)$

Answer 1

The correct option is B

$\mathrm{A}\text{'}(1,2),\mathrm{B}\text{'}(1,-1),\mathrm{C}\text{'}(3,-1)$

Find the coordinates of image after translation.

Given, figure

From given figure, we have given coordinates as,

$\mathrm{A}(-2,4),\mathrm{B}(-2,1),\mathrm{C}(0,1)$ and the parameters are $\mathrm{a}=3,\mathrm{b}=-2$

As we know that 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 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.

Using the above criteria of translation.

$$\begin{gathered} \mathrm{A}(-2,4)=\mathrm{A}\text{'}(-2+3,4-2)=\mathrm{A}\text{'}(1,2) \\ \mathrm{B}(-2,1)=\mathrm{B}\text{'}(-2+3,1-2)=\mathrm{B}\text{'}(1,-1) \\ \mathrm{C}(0,1)=\mathrm{C}\text{'}(0+3,1-2)=\mathrm{C}\text{'}(3,-1) \end{gathered}$$

Hence, the coordinate of the image after transformation are $\mathrm{A}\text{'}(1,2),\mathrm{B}\text{'}(1,-1),\mathrm{C}\text{'}(3,-1)$ and correct option is (B).