# Lesson Worksheet: Linear Transformations in Planes: Scaling Mathematics • 10th Grade

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 at 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 at the origin
• BA dilation with scale factor 3 and center at the origin
• CA stretch in the -direction
• DA stretch in the -direction
• EA rotation about the origin by an angle of