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Linear Transformations Worksheet

Explore linear transformations including translations, rotations, reflections, and dilations on a coordinate plane.

Grade 9 Math AlgebraLinear Transformation
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5 Short AnswerMultiple ChoiceFill in the Blanks

Standards

CCSS.MATH.CONTENT.HSG.CO.A.2CCSS.MATH.CONTENT.HSG.CO.A.4CCSS.MATH.CONTENT.HSG.SRT.A.1

Topics

MathAlgebraLinear TransformationGeometryGrade 9
9 sections · Free to use · Printable
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Linear Transformations Worksheet

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Read each question carefully and follow the instructions to perform the linear transformations. Show all your work on the coordinate planes provided.

1. Translate the triangle with vertices A(1,1), B(3,1), and C(2,3) by the vector <2, -3>. Plot the original and transformed triangles on the graph below.

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2. Reflect the square with vertices P(-4,2), Q(-2,2), R(-2,4), and S(-4,4) across the y-axis. Plot both the original and reflected squares on the graph.

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3. Rotate the segment with endpoints D(1, -2) and E(3, -4) 90 degrees clockwise about the origin. Plot the original and rotated segments.

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4. Dilate the rectangle with vertices F(-2, -1), G(2, -1), H(2, -3), and I(-2, -3) by a scale factor of 2 with the center of dilation at the origin. Plot both the original and dilated rectangles.

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5. Which type of transformation changes the size of a figure?

a

Translation

b

Rotation

c

Reflection

d

Dilation

6. A   is a transformation that slides a figure from one position to another without turning it.

7. A   is a transformation that flips a figure over a line.

8. Describe the sequence of transformations (translation, reflection, rotation, dilation) that maps triangle ABC with vertices A(1,1), B(3,1), C(2,3) to triangle A''B''C'' with vertices A''(-4,-2), B''(-2,-2), C''(-3,-4).