Transformation Blueprint Reviewer
Transformation Blueprint
Mastery Assessment Practice Test
Project ID: GEO-2026-TR
Drafted By (Student Name)
Date of Analysis
01
Point \( A(4, -3) \) is translated using the rule \( (x, y) \to (x - 5, y + 2) \). What are the coordinates of the image \( A' \)?
A) \( (9, -1) \)
B) \( (-1, -1) \)
C) \( (-1, -5) \)
D) \( (1, 1) \)
02
Which translation vector moves a point 4 units to the right and 7 units down?
A) \( \langle -4, 7 \rangle \)
B) \( \langle 7, -4 \rangle \)
C) \( \langle 4, -7 \rangle \)
D) \( \langle -7, 4 \rangle \)
03
If point \( P(-2, 6) \) is reflected across the x-axis, what are the coordinates of \( P' \)?
A) \( (2, 6) \)
B) \( (-2, -6) \)
C) \( (2, -6) \)
D) \( (6, -2) \)
04
Coordinate Mapping Task
Reflect the triangle with vertices \( L(1, 2), M(4, 2), N(3, 5) \) over the line \( y = x \). Provide coordinates.
L': (____, ____) M': (____, ____) N': (____, ____)
05
A transformation maps \( (3, 7) \to (3, -7) \). This is a reflection over the:
A) y-axis
B) x-axis
C) line \( y = x \)
D) origin
Phase III & IV: Rotations & Dilations
06
Rotate point \( B(3, -5) \) 90° counterclockwise about origin. What is the new location?
A) \( (5, 3) \)
B) \( (-5, -3) \)
C) \( (-3, 5) \)
D) \( (3, 5) \)
07
Which rule represents a rotation of 180° about the origin?
A) \( (x, y) \to (-y, x) \)
B) \( (x, y) \to (y, -x) \)
C) \( (x, y) \to (-x, -y) \)
D) \( (x, y) \to (y, x) \)
08
Standard Position Check
Point \( (3, 1) \) is rotated 270° counterclockwise about origin. New coordinates?
P': (_____, _____)
09
Point \( C(-4, 2) \) is dilated by \( k = 1.5 \) with center \( (0,0) \). Coordinates of \( C' \)?
A) \( (-6, 3) \)
B) \( (-2.5, 0.5) \)
C) \( (-4.5, 3.5) \)
D) \( (-8, 4) \)
10
A segment length of 12 is dilated by \( k = 1/4 \). What is the image length?
A) 48 units
B) 3 units
C) 6 units
D) 12 units
Phase V & VI: Compositions & ID
11
Which of the following is NOT a rigid motion (isometry)?
A) Translation
B) Rotation
C) Dilation
D) Reflection
12
\( D(2, 4) \) reflected over y-axis, then translated by \( \langle 3, -2 \rangle \). Final location?
A) \( (1, 2) \)
B) \( (5, 2) \)
C) \( (-5, 6) \)
D) \( (1, 6) \)
13
A glide reflection is a composition of which two transformations?
A) Dilation and Translation
B) Rotation and Reflection
C) Translation and Reflection
D) Rotation and Dilation
14
Compound Trajectory
Point \( A(1, -2) \) is dilated by \( k=2 \) centered at origin, then rotated 180° about origin. Final coordinates \( A'' \)?
A'': (_____, _____)
15
If point \( (x, y) \) becomes \( (-y, -x) \), what single transformation occurred?
A) Reflection over \( y = -x \)
B) Rotation 180°
C) Reflection over \( y = x \)
D) Rotation 90° clockwise
Phase VII: Final Evaluation
16
What is the scale factor \( k \) of a dilation that maps \( (4, 10) \to (2, 5) \)?
A) \( k = 2 \)
B) \( k = -2 \)
C) \( k = 1/2 \)
D) \( k = 1/4 \)
17
Which sequence of transformations will map a figure in Quadrant I back to Quadrant I?
A) Refl x then Refl y
B) Rot 180 then Refl Orig
C) Refl \(y=x\) then Refl \(y=-x\)
D) Translation \(\langle -10,-10 \rangle\)
18
Advanced Blueprint Analysis
Reflect point \( M(-1, 3) \) over the line \( x = 2 \). Show your logical process or distance analysis below.
Process Log / Logic Field
Final Coordinate Result: (_____, _____)
19
Which of the following rotations is equivalent to a rotation of 90° clockwise?
A) 90° CCW
B) 270° CCW
C) 180° CW
D) 270° CW
20
Dilate \( \triangle ABC \) by \( k=3 \). If the area of \( \triangle ABC \) is 5, what is the area of the image \( \triangle A'B'C' \)?
A) 15 units²
B) 45 units²
C) 8 units²
D) 25 units²
End of Technical Assessment
Project Certified: Geometry Mastery 2026 | Blueprint Ver. 2.0
Transformation Blueprint Key
MASTER KEY: TRANSFORMATIONS
Teacher Evaluation Reference
VERSION 2.0
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B \( (-1, -1) \)
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C \( \langle 4, -7 \rangle \)
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B \( (-2, -6) \)
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L'(2,1), M'(2,4), N'(5,3)
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B x-axis
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A \( (5, 3) \)
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C \( (-x, -y) \)
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\( (1, -3) \)
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A \( (-6, 3) \)
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B 3 units
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C Dilation
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A \( (1, 2) \)
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C Trans + Refl
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\( (-2, 4) \)
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A \( y = -x \)
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C \( k = 1/2 \)
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B Rot 180 + Refl
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\( (5, 3) \)
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B 270° CCW
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B 45 units²
Technical Breakdown & Proofs
Q08 Rotation: Rule for 270 deg CCW: (x, y) → (y, -x). The input (3, 1) results in the output (1, -3).
Q14 Composition: Dilation by k=2 on (1, -2) yields (2, -4). Subsequent 180 deg rotation [(x,y) → (-x,-y)] results in (-2, 4).
Q18 Mastery Task: Reflection of M(-1, 3) over vertical line x=2. Horizontal distance is 3 units to the left. The image is 3 units to the right of the axis (2 + 3 = 5). Result: (5, 3).
Q20 Dilation Area: New Area = Original × k². Given k=3, Area = 5 × 3² = 5 × 9 = 45 units².
Internal Reference Only | Geometry Faculty 2026
