Transformation Review Worksheet Math 8 • Geometry Practice Assessment
Transformation Review Practice
Rigid Motions, Dilations, and Similar Figures
Name:
Date: Period:
1
Single Point Transformations & Plotting
Plot Points \(A', B', C', D'\)
x y 5 -5 5 -5 A B C D
Pre-images \(A, B, C, D\) are plotted
Find the coordinates of each transformed point, then plot and label \(A', B', C',\) and \(D'\) on the grid:
1. Translation
Point \(A(2, -3)\) by \((x - 5, \; y + 4)\)
\(A'\): ( , )
2. Reflection
Point \(B(-4, 3)\) across the x-axis
\(B'\): ( , )
3. Reflection
Point \(C(5, 2)\) across the y-axis
\(C'\): ( , )
4. Rotation
Point \(D(-3, -2)\) rotated \(90^\circ\) clockwise about \((0,0)\)
\(D'\): ( , )
2
Shape Dilation on the Coordinate Plane
Pre-Image \(\triangle JKL\)
x y 3 -3 3 -3 J K L
Scale: 1 square = 1 unit
\(\triangle JKL\) has vertices \(J(1, 1)\), \(K(3, 1)\), and \(L(1, 3)\). Dilate \(\triangle JKL\) using a scale factor of \(k = 2\) with the origin as the center of dilation.
A. Record the coordinates of the dilated image \(\triangle J'K'L'\):
\(J'\):
( , )
\(K'\):
( , )
\(L'\):
( , )
B. Graph: Plot and label points \(J'\), \(K'\), and \(L'\) on the grid above to form \(\triangle J'K'L'\).
C. Side Length Comparison:
Length of \(JK\) = units
Length of \(J'K'\) = units
D. Is \(\triangle J'K'L'\) congruent or similar to \(\triangle JKL\)? Explain your reasoning.
8th Grade Mathematics Page 1 of 2 Turn to Page 2 →
Sequences, Similarity & Rotations
Transformation Review Practice • Page 2
Classwork / Homework
3
Sequence of Two Transformations & Graphing
Plot \(\triangle P'Q'R'\) and \(\triangle P''Q''R''\)
x y P Q R
Pre-Image: \(P(1,1), Q(4,1), R(1,3)\)
Follow the sequence, then graph each figure on the grid:
Step 1: Reflect across the y-axis . Record coordinates below and plot \(\triangle P'Q'R'\) .Step 2: Translate \(\triangle P'Q'R'\) down 4 units . Record coordinates below and plot \(\triangle P''Q''R''\) .
Original After Step 1 (Reflect) After Step 2 (Translate) \(P(1, 1)\) \(P'(\) , \()\) \(P''(\) , \()\) \(Q(4, 1)\) \(Q'(\) , \()\) \(Q''(\) , \()\) \(R(1, 3)\) \(R'(\) , \()\) \(R''(\) , \()\)
Is the final image \(\triangle P''Q''R''\) congruent or similar to \(\triangle PQR\)? Explain why:
4
Similar Shapes & Proportional Sides
Figure A (Original) width = 3 cm 4 cm
Dilation (factor = k)
Figure B (Dilated) width = 9 cm \(h =\) ?
Problem 4A: Scale Factor
Find the scale factor from Figure A to Figure B.
Show work:
Scale factor \(k =\)
Problem 4B: Missing Dimension
Calculate the missing height (\(h\)) of Figure B.
Show work:
Height \(h =\) cm
5
Shape Rotation (\(180^\circ\) about Origin)
Plot Image \(\triangle M'N'P'\)
x y M N P
Pre-Image: \(M(-4,1), N(-1,1), P(-2,4)\)
Rotate \(\triangle MNP\) by \(180^\circ\) about the origin \((0,0)\) to produce \(\triangle M'N'P'\).
A. Record the coordinates of image \(\triangle M'N'P'\):
\(M'\): ( , )
\(N'\): ( , )
\(P'\): ( , )
B. Graph: Plot and connect points \(M'\), \(N'\), and \(P'\) on the grid to draw \(\triangle M'N'P'\).
C. Is a \(180^\circ\) rotation a rigid motion? Explain:
8th Grade Mathematics • Congruence & Similarity Page 2 of 2 Completed
Transformation Review Answer Key Teacher Reference FULL ANSWER KEY
Transformation Review Answer Key
Detailed Solutions, Graph Solutions & Explanations
Standard: CCSS 8.G.A.1, 8.G.A.3, 8.G.A.4 Rigid & Non-Rigid Motions
1
Single Point Transformations & Plotting Solutions
Plotted Image Solutions (\(A', B', C', D'\))
x y 5 -5 5 -5 A B C D A'(-3, 1) B'(-4, -3) C'(-5, 2) D'(-2, 3)
Pre-images (gray) • Images (green)
1. Translation Rule: \((x-5, y+4)\)
\(A(2, -3) \rightarrow (2 - 5, \; -3 + 4)\)
\(A'\): (-3, 1)
2. Reflection x-axis: \((x, -y)\)
\(B(-4, 3) \rightarrow (-4, \; -(3))\)
\(B'\): (-4, -3)
3. Reflection y-axis: \((-x, y)\)
\(C(5, 2) \rightarrow (-(5), \; 2)\)
\(C'\): (-5, 2)
4. Rotation \(90^\circ\) CW: \((y, -x)\)
\(D(-3, -2) \rightarrow (-2, \; -(-3))\)
\(D'\): (-2, 3)
2
Shape Dilation Solution & Graph Overlay
\(\triangle JKL\) & Dilated \(\triangle J'K'L'\)
x y J K L J'(2,2) K'(6,2) L'(2,6)
Dilation centered at \((0,0)\), \(k=2\)
A. Image Coordinates \((k = 2 \implies 2x, 2y)\):
\(J'\): (2, 2)
\(K'\): (6, 2)
\(L'\): (2, 6)
B. Graph Check: Vertices are plotted at \((2,2), (6,2),\) and \((2,6)\). The shape is scaled by factor 2 from origin.
C. Side Length Comparison:
Length of \(JK\) = 2 units (\(3 - 1 = 2\))
Length of \(J'K'\) = 4 units (\(2 \times 2 = 4\))
D. Congruent or Similar? Explanation:
SIMILAR (not congruent). Dilations change the size of the shape by multiplying all side lengths by the scale factor (\(k = 2\)), while preserving angle measures. Because the side lengths changed from 2 to 4, the figures are similar but not congruent.
8th Grade Geometry • Answer Key Page 1 of 2 Turn to Page 2 Solutions →
Sequences, Similarity & Rotations Solutions
Transformation Review Answer Key • Page 2
Teacher Grading Key
3
Sequence of Two Transformations Solutions
Graph Solutions: \(\triangle PQR, P', P''\)
x y P P' Q' R' P'' Q'' R''
Final: \(\triangle P''Q''R''\) in Quad III
Original Step 1: Reflect y-axis \((-x, y)\) Step 2: Translate \((x, y-4)\)
Transformation Rules Review Slides 8th Grade Geometry Review Rigid & Non-Rigid Motions
Transformation Motions & Similarity
Visual coordinate graphs for translations, reflections, rotations, and dilations.
Translation Slide
Reflection Flip
Rotation Turn
Dilation Resize
1
Translations: Slide / Shift
Rigid Motion • Congruent
Coordinate Rule
\((x, y) \rightarrow (x + a, \; y + b)\)
Example: \(P(3, -2) \rightarrow (x - 4, \; y + 5)\)
• Shift Left 4: \(3 - 4 = -1\)
• Shift Up 5: \(-2 + 5 = 3\)
New Point: \(P'(-1, 3)\)
Motion Path on Coordinate Plane x y P(3, -2) P'(-1, 3)
Add or subtract coordinates directly • Size and angles stay strictly congruent!
2
Reflections: Flip Across an Axis
Rigid Motion • Congruent
Over x-axis \(A(3, \mathbf{2}) \rightarrow A'(3, \mathbf{-2})\)
\((x, y) \rightarrow (x, -y)\)
x-axis A(3, 2) A'(3, -2)
Over y-axis \(B(\mathbf{-3}, 2) \rightarrow B'(\mathbf{3}, 2)\)
\((x, y) \rightarrow (-x, y)\)
y-axis B(-3, 2) B'(3, 2)
Flip over an axis → The opposite coordinate flips its positive/negative sign!
3
Rotations: Turn About Origin \((0,0)\)
Rigid Motion • Congruent
\(90^\circ\) Clockwise \(C(2, 4) \rightarrow C'(4, -2)\)
\((x, y) \rightarrow (y, -x)\)
C(2, 4) C'(4, -2) 90°
\(180^\circ\) Half Turn \(D(-3, 2) \rightarrow D'(3, -2)\)
\((x, y) \rightarrow (-x, -y)\)
D(-3, 2) D'(3, -2) 180°
Rotations turn figures around \((0,0)\) • Distance from the origin is preserved!
4
Dilations: Resize with Scale Factor \(k\)
Non-Rigid • Similar Figures
Coordinate Rule
\((x, y) \rightarrow (k \cdot x, \; k \cdot y)\)
• If \(k > 1\) : Shape Enlarges (grows bigger)
• ✓ Angles: Stay strictly EQUAL (Congruent)
• ✗ Side Lengths: Multiplied by \(k\)
• Resulting shapes are SIMILAR (not congruent)
Graph: Triangle Dilation with \(k = 2\) (0,0) J K L J'(2,2) K'(4,2) L'(2,4)
