Question

on the graph below, the translation vector ( select select ) maps δabc to δabc.

Explanation:

Step1: Find the change in x-coordinate

To find the horizontal component of the translation vector, we subtract the x-coordinate of a point in \( \triangle ABC \) from the x-coordinate of the corresponding point in \( \triangle A'B'C' \). Let's use point \( A \): \( x \)-coordinate of \( A \) is \( 3 \), \( x \)-coordinate of \( A' \) is \( -7 \). So the change in \( x \) is \( -7 - 3=-10 \).

Step2: Find the change in y-coordinate

To find the vertical component of the translation vector, we subtract the y-coordinate of a point in \( \triangle ABC \) from the y-coordinate of the corresponding point in \( \triangle A'B'C' \). Using point \( A \): \( y \)-coordinate of \( A \) is \( 1 \), \( y \)-coordinate of \( A' \) is \( -3 \). So the change in \( y \) is \( -3 - 1 = -4 \).

Answer:

The translation vector is \(

$$\begin{pmatrix}-10\\-4\end{pmatrix}$$

\) (or in the form of \( (-10, -4) \) depending on the required notation for the translation vector).