How many practice questions are available for Transformations?

SparkEd Math offers 60+ practice questions for Transformations across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Transformations content free on SparkEd Math?

Yes! All Transformations content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Transformations differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Transformations problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Transformations content aligned with the IB syllabus?

Yes, all Transformations questions and lessons on SparkEd Math are fully aligned with the International Baccalaureate (MYP) (IB) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Transformations — Class 7 IB (2025-26)

About Transformations — Class 7 IB

Perform translations, reflections, and rotations of shapes on the coordinate plane. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 6). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Transformations

Introduction to Translations
Reflections
Rotations
Describing Transformations
Congruence and Combined Transformations

Interactive lesson · about 75 minutes · checkpoint question after every unit

Transformations — solved examples for Class 7 IB

Example 1easy

A point P has coordinates (3, -2). It is translated by the vector $\begin{pmatrix} -4 \\ 5 \end{pmatrix}$. What are the new coordinates of P'?

A)(7, 3)
B)(-1, 3)
C)(1, 7)
D)(-1, -7)

Step-by-step solution

Identify the original coordinates of P: (3, -2).
$P = (x, y) = (3, -2)$
Identify the translation vector: $\begin{pmatrix} -4 \\ 5 \end{pmatrix}$.
$Vector = $\begin{pmatrix} a \\ b \end{pmatrix}$ = $\begin{pmatrix} -4 \\ 5 \end{pmatrix}$$
Apply the translation rule (x+a, y+b).
$P' = (3 + (-4), -2 + 5)$
Calculate the new coordinates.
$P' = (-1, 3)$

Answer: (-1, 3)

Example 2medium

A triangular logo has vertices at A(1, 2), B(4, 2), and C(1, 5). If the logo is translated by the vector \begin{pmatrix} -3 \\ 4 \end{pmatrix}, what are the new coordinates of vertex B'?

A)A. (7, -2)
B)B. (1, 6)
C)C. (4, 6)
D)D. (7, 2)

Step-by-step solution

Identify the original coordinates of vertex B.
$B = (4, 2)$
Identify the translation vector.
$\begin{pmatrix} -3 \\ 4 \end{pmatrix}$
Add the x-component of the vector to the x-coordinate of B, and the y-component to the y-coordinate of B to find B'.
$B' = (4 + (-3), 2 + 4) = (1, 6)$

Answer: B. (1, 6)

Example 3hard

A triangular flag, ΔPQR, is translated by the vector T = (3, -5) to form its image, ΔP'Q'R'. If the coordinates of P' are (-2, 4), what were the original coordinates of P?

A)(-5, 9)
B)(1, -1)
C)(6, -1)
D)(-2, 4)

Step-by-step solution

Let the original coordinates of P be (x, y).
$P(x, y)$
When P(x, y) is translated by the vector T = (3, -5), its image P' is (x+3, y-5).
$P'(x+3, y-5)$
We are given that P' is (-2, 4). So, we can set up two equations:
$x + 3 = -2 AND y - 5 = 4$
Solving for x: x = -2 - 3 = -5. Solving for y: y = 4 + 5 = 9. Therefore, the original coordinates of P were (-5, 9).
$P(-5, 9)$

Answer: (-5, 9)

Practice questions on Transformations

Q1.easy
A triangle with vertices A(1, 4), B(3, 1), and C(5, 4) is reflected across the x-axis. What are the coordinates of the reflected vertex A'?
1. A)(-1, 4)
2. B)(1, -4)
3. C)(-1, -4)
4. D)(4, 1)
Show answer
Answer: (1, -4)
Hint: When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes its sign.
Q2.easy
A point Q is located at (-2, 5). What are the coordinates of Q' after a 90° clockwise rotation about the origin?
1. A)(5, 2)
2. B)(-5, -2)
3. C)(2, -5)
4. D)(5, -2)
Show answer
Answer: (5, 2)
Hint: For a 90° clockwise rotation about the origin, the rule is (x, y) → (y, -x).
Q3.easy
A small toy car moves from its starting position at (2, 1) to a new position at (-1, 3) on a coordinate map. Which single transformation best describes its movement?
1. A)Reflection in the y-axis
2. B)Rotation 90° counter-clockwise about the origin
3. C)Translation by vector $\begin{pmatrix} -3 \\ 2 \end{pmatrix}$
4. D)Translation by vector $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$
Show answer
Answer: Translation by vector $\begin{pmatrix} -3 \\ 2 \end{pmatrix}$
Hint: Compare the change in x-coordinates and y-coordinates to determine the components of the translation vector.
Q4.medium
A drone is located at coordinates (-5, 3). It performs a manoeuvre that reflects its position across the y-axis. What are the new coordinates of the drone?
1. A)A. (-5, -3)
2. B)B. (5, -3)
3. C)C. (5, 3)
4. D)D. (3, -5)
Show answer
Answer: C. (5, 3)
Hint: When reflecting a point across the y-axis, the x-coordinate changes its sign, while the y-coordinate remains the same.
Q5.medium
A security camera at the origin (0,0) captures an object at point P(2, -4). If the camera rotates 90° anti-clockwise about the origin, what would be the coordinates of the object's new relative position, P'?
1. A)A. (4, 2)
2. B)B. (-2, 4)
3. C)C. (-4, -2)
4. D)D. (2, 4)
Show answer
Answer: A. (4, 2)
Hint: For a 90° anti-clockwise rotation about the origin, the rule is to swap the coordinates and change the sign of the new x-coordinate.
Q6.medium
A cargo ship moved from its initial position at (7, -2) to a new position at (3, 1). Which vector represents the translation the ship underwent?
1. A)A. \begin{pmatrix} 4 \\ -3 \end{pmatrix}
2. B)B. \begin{pmatrix} 10 \\ -1 \end{pmatrix}
3. C)C. \begin{pmatrix} -4 \\ -3 \end{pmatrix}
4. D)D. \begin{pmatrix} -4 \\ 3 \end{pmatrix}
Show answer
Answer: D. \begin{pmatrix} -4 \\ 3 \end{pmatrix}
Hint: To find the translation vector, subtract the initial coordinates from the final coordinates.
Q7.hard
Point A(3, 7) is reflected across a line L to form its image A'(9, 1). What is the equation of the line L?
1. A)y = -x + 10
2. B)y = x + 2
3. C)y = -x + 12
4. D)y = x + 4
Show answer
Answer: y = x + 2
Hint: The line of reflection is the perpendicular bisector of the segment connecting the pre-image and its image.
Q8.hard
A design motif at point M(5, -2) is rotated 90° clockwise about the origin to M'. Then, M' is rotated 180° about the origin to M''. Which single rotation maps M to M''?
1. A)90° anti-clockwise about the origin
2. B)270° clockwise about the origin
3. C)90° clockwise about the origin
4. D)270° anti-clockwise about the origin
Show answer
Answer: 270° clockwise about the origin
Hint: Consider the total angle of rotation. Remember that a 90° clockwise rotation is equivalent to a -90° rotation, and 180° is invariant to direction.
Q9.hard
A square is first translated by the vector T = (a, b) where a ≠ 0 and b ≠ 0. Then, its image is reflected in the y-axis. Which of the following properties of the square *must* change after these two transformations?
1. A)Its area
2. B)Its perimeter
3. C)The orientation of its vertices (e.g., clockwise/anti-clockwise order)
4. D)The x-coordinates of all its vertices
Show answer
Answer: The x-coordinates of all its vertices
Hint: Consider what happens to the coordinates under each transformation. Rigid transformations preserve shape and size.

These are 9 of the 60 questions available for Transformations. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.