Question

translate the figure 2 units left and 1 unit down. draw a vector from the origin 2 units left and 1 unit down.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ in the coordinate - plane, translating it $a$ units left and $b$ units down gives the new point $(x - a,y - b)$. Here $a = 2$ and $b = 1$.

Step2: Translate each vertex

Let the vertices of the original polygon be $(x_1,y_1),(x_2,y_2),\cdots$. The new vertices will be $(x_1-2,y_1 - 1),(x_2-2,y_2 - 1),\cdots$.

Step3: Plot the new figure

Connect the new vertices to get the translated figure.

To draw the vector from the origin, start at the point $(0,0)$ and end at the point $(- 2,-1)$.

Answer:

To translate the figure, subtract 2 from the $x$ - coordinates and 1 from the $y$ - coordinates of all its vertices. The vector from the origin for the translation has an initial point at $(0,0)$ and a terminal point at $(-2,-1)$.