# 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