Question

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 subtracted from the first matrix? transform=⎡⎣⎢202020−20−20−20⎤⎦⎥ (1 point) Responses A translation to the left by 20 units and up by 20 units. A translation to the left by 20 units and up by 20 units. A flip over the y-axis. A flip over the y -axis. A translation to the left by 20 units and down by 20 units. A translation to the left by 20 units and down by 20 units. A translation to the right by 20 units and down by 20 units.

Answer 1

To determine the transformation represented by subtracting the given matrix \( \begin{bmatrix} 20 \ 20 \ -20 \ -20 \end{bmatrix} \) from the triangle coordinates matrix, let's first analyze what each component of the transformation matrix signifies:

The transformation matrix is structured as follows:

\[ \text{transform} = \begin{bmatrix} 20 & 20 \ -20 & -20 \end{bmatrix} \]

When we subtract a transformation matrix like this from the coordinates matrix of the triangle, we treat the operation as modifying each vertex of the triangle.

Effect of the matrix:

• The first column (20) indicates that we are adding 20 to the x-coordinates. Subtracting it from the first column means we're actually translating each x-coordinate to the left by 20 units.
• The second column (20) indicates that we are adding 20 to the y-coordinates. Subtracting it means we are translating each y-coordinate downward by 20 units.

Thus, the overall result of subtracting this matrix from the triangle's coordinate matrix is:

• A translation to the left by 20 units (for the x-coordinates).
• A translation down by 20 units (for the y-coordinates).

Based on the above analysis, the correct transformation that is represented by this operation is:

A translation to the left by 20 units and down by 20 units.