Transformation Tactics Reference Sheet
Transformation Tactics
Reference Sheet // Unit: Geometry 7.G.A.2
Agent Name
Date
Geometric transformations are movements of shapes on a coordinate plane. Use these checklists to ensure your "Prime" shapes (A′, B′, C′) are plotted with absolute precision.
1. Translations (Slides)
Mission Checklist
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Identify the Rule: Find the x change (left/right) and y change (up/down). Rule format: (x ± a, y ± b).
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Move Every Vertex: Start at each point of the original shape (Pre-image). Slide it the exact distance and direction.
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Label the Image: Name new points using "prime" notation (e.g., A → A′).
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Verify Congruence: Does the new shape look identical to the old one? It should not change size or turn!
Visual Logic: Slide Vector
Pre Prime
"A translation moves the whole shape without turning it."
2. Reflections (Flips)
Mission Checklist
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Locate the Mirror Line: Usually the x-axis or y-axis. Highlight it on your graph!
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Measure the Distance: For one point, count how many units it is from the mirror line.
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Plot the Mirror Point: Count the same distance on the opposite side of the line and plot the point.
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Verify Orientation: The shape should be "flipped." Right becomes left, or top becomes bottom!
Quick Coordinate Rules
Reflect over x-axis: (x, -y)
Reflect over y-axis: (-x, y)
Note: If a point is on the axis, it stays exactly where it is.
3. Rotations (Turns)
Mission Checklist
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Determine Direction: Clockwise (CW) or Counter-Clockwise (CCW)?
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Find the Degree: 90° (1 turn), 180° (2 turns), or 270° (3 turns).
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Apply the Rule: Use the coordinate formulas below to find new points.
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Check the Quadrant: A 90° CW turn moves a shape from one quadrant to the next.
90° CW / 270° CCW
(y, -x)
Switch values, then flip the sign of the 2nd.
Most Common
180° Rotation
(-x, -y)
Keep order, just flip both signs!
270° CW / 90° CCW
(-y, x)
Switch values, then flip the sign of the 1st.
Shape Shifting Practice Worksheet
Shape Shifting Practice
Mission Field Manual // Transformations Practice
Agent Name
Date
1
Mission: The Slide
Translate Triangle ABC with vertices:
A(1, 2), B(4, 2), C(1, 5)
Rule: (x + 3, y - 4)
Checklist Steps
Identify shift (3 Right, 4 Down)
Plot new vertices A′, B′, C′
New Coordinates
A′
B′
C′
x y 1 4 1 5 A B C
2
Mission: The Flip
Reflect Rectangle JKLM across the y-axis.
Vertices: J(2, 1), K(5, 1), L(5, 3), M(2, 3)
Checklist Steps
Highlight the Y-Axis
Apply Rule: (-x, y)
New Coordinates
J′
K′
L′
M′
J K L M
3
Mission: The Pivot
Rotate Shape PQRS by 180° about the origin.
Vertices: P(2, -1), Q(4, -1), R(4, -3), S(2, -3)
Checklist Steps
Apply Rule: (x, y) → (-x, -y)
Plot new vertices in the opposite quadrant
New Coordinates
P′
Q′
R′
S′
P Q R S
