Worksheet: Linear Transformations in Planes: Scaling
In this worksheet, we will practice finding the matrix that scales a vector by a given scaling factor and the image of the vector under scaling linear transformation.
Q1:
Consider the transformation represented by the matrix
What is the image of the square with vertices , , , and under this transformation?
- Aa kite with vertices , and
- Ba kite with vertices , and
- Ca square with vertices , , , and
- Da square with vertices , , , and
- Ea square with vertices , , , and
What geometric transformation does this matrix represent?
- Aa stretch in the -direction
- Ba stretch in the -direction
- Ca rotation about the origin by an angle of
- Da dilation with scale factor 3 and center the origin
- Ea dilation by a factor of 3 with its center at the point
Q2:
Consider the transformation represented by the matrix
What is the image of the square with vertices , , , and under this transformation?
- Aa square with vertices , , , and
- Ban arrowhead with vertices , and
- Ca kite with vertices , and
- Dan arrowhead with vertices , and
- Ea square with vertices , , , and
What geometric transformation does this matrix represent?
- Aa dilation with scale factor and center the origin
- Ba dilation with scale factor 3 and center the origin
- Ca stretch in the -direction
- Da stretch in the -direction
- Ea rotation about the origin by an angle of