Question

The vertices of a triangle are $\mathrm{A}(-1,-2),\mathrm{B}(-2,2),$ and $\mathrm{C}(-3,0)$. Draw the figure and its image after a translation $5$ unit's right and $1$unit Up.

Answer 1

Step 1: Find the coordinates after translation.$\mathrm{A}\text{'}(4,-1),\mathrm{B}\text{'}(3,3),\mathrm{C}\text{'}(2,1)$

Given, coordinates are $\mathrm{A}(-1,-2),\mathrm{B}(-2,2),$ and $\mathrm{C}(-3,0)$

also, $\mathrm{a}=5\mathrm{and}\mathrm{b}=1$

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.

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

The value of $\text{'}\mathrm{a}\text{'}$ and $\text{'}\mathrm{b}\text{'}$ will be positive if shift is right and vertical 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, we have

$$\begin{gathered} \mathrm{A}(-1,-2)=\mathrm{A}\text{'}(-1+5,-2+1)=\mathrm{A}\text{'}(4,-1) \\ \mathrm{B}(-2,2)=\mathrm{B}\text{'}(-2+5,2+1)=\mathrm{B}\text{'}(3,3) \\ \mathrm{C}(-3,0)=\mathrm{C}\text{'}(-3+5,0+1)=\mathrm{C}\text{'}(2,1) \end{gathered}$$

Step 2: draw the figure

Step 3: Final answer.

Hence, the coordinates after translation is