Question

The vertices of a triangle are $\mathrm{A}(-2,-2),\mathrm{B}(0,2)$ and $\mathrm{C}(3,0)$. Translate the triangle $1$unit left and $2$ units up. What are the co-ordinates of the image.

Answer 1

Step 1: Translation of triangle.

Given, the coordinates of a triangle are $\mathrm{A}(-2,-2),\mathrm{B}(0,2)$ and $\mathrm{C}(3,0)$.

And we have to translate the triangle $1$unit left and $2$ units up,

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.

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

Then, after translation initial point becomes will be

$\Rightarrow \mathrm{A}(\mathrm{x},\mathrm{y})=\mathrm{A}\text{'}(\mathrm{x}-\mathrm{a},\mathrm{y}+\mathrm{b})$, similarly to others.

where, $\mathrm{a}=1$ and $\mathrm{b}=2$.

Step 2: Find the new coordinates of the triangle.

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

Step 3. Plotting of coordinates.

Hence, the new coordinates will be $\mathrm{A}\text{'}(-3,0)\mathrm{B}\text{'}(-1,4)$ and $\mathrm{C}\text{'}(2,2)$,