The given matrix is:
$$
\begin{bmatrix}
-20 & -10 \\
-10 & 0 \\
\end{bmatrix}
$$
To understand the transformation represented by this matrix, we need to add it to the matrix representing the original triangle. Let's call the original matrix $M$:
$$
M = \begin{bmatrix}
x_A & y_A \\
x_B & y_B \\
x_C & y_C \\
\end{bmatrix}
$$
To add the given matrix to $M$, we add the corresponding entries:
$$
\begin{bmatrix}
x_A - 20 & y_A - 10 \\
x_B - 20 & y_B - 10 \\
x_C - 20 & y_C - 10 \\
\end{bmatrix}
$$
This means that all the points of the original triangle have been shifted to the left by 20 units and down by 10 units. Therefore, the transformation represented by the given matrix is a translation to the left by 20 units and down by 10 units.
So the answer is (C) a translation to the left by 20 units and down by 10 units.
The coordinates of a triangle are described by a matrix, where the rows represent each point, A, B, and C, from top row to bottom row, and column 1 represents the x coordinates and column 2 represents the y coordinates. What transformation does the following matrix represent when added to the first matrix?
A. A rotation about the origin clockwise by 90°
B. A flip over the y-axis
C. A translation to the left by 20 units and down by 20 units
D. A translation to the right by 20 units and down by 20 units
1 answer