Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.143

Pre CAL.143 Use Matrices to Represent Rotations and Dilations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.143 Use Matrices to Represent Rotations and Dilations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.143 Use Matrices to Represent Rotations and Dilations - Use Matrices to Represent Rotations and Dilations

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.143 Use Matrices to Represent Rotations and Dilations skill assessments:

Problem 1Difficulty: Mastery

A transformation rotates 30 degrees counterclockwise and dilates by factor 2. What is the image of (1, 0)? (Use cos30=0.866 and sin30=0.500.)

A(1.732, -1.000)

B(1.732, 1.000)

C(0.866, 0.500)

D(2.000, 0.000)

Solution & Explanation:The matrix is 2[[0.866,-0.500],[0.500,0.866]]. Apply to (1,0): (2*0.866, 2*0.500) = (1.732, 1.000).

Problem 2Difficulty: Mastery

The matrix [[0, -3], [3, 0]] represents 'rotate 90 degrees counterclockwise, then dilate by 3'. Which matrix represents the inverse transformation? (Round 1/3 to 0.333.)

A[[0, -0.333], [0.333, 0]]

B[[0, 3], [-3, 0]]

C[[0, -3], [3, 0]]

D[[0, 0.333], [-0.333, 0]]

Solution & Explanation:The inverse undoes the dilation and the rotation: rotate 90 degrees clockwise and dilate by 0.333. So the inverse matrix is 0.333[[0,1],[-1,0]] = [[0,0.333],[-0.333,0]].

Problem 3Difficulty: Mastery

Let A = [[1.732, -1.000], [1.000, 1.732]]. The image point is A(x, y) = (0.000, 3.464). Which ordered pair could be (x, y)? (Values rounded to 3 decimals.)

A(0.866, 1.500)

B(0.866, -1.500)

C(-0.866, 1.500)

D(1.500, 0.866)

Solution & Explanation:Solve A(x,y)=(0,3.464). Because A is invertible (a rotation+dilation), the solution is (x,y)≈(0.866, 1.500).

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard Pre-CAL.143 (Use Matrices to Represent Rotations and Dilations).