MathsFreePrintable

Combined Transformations Practice

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Combined Transformations Practice

A robotics team is testing how a shape moves across a coordinate plane. Work through each transformation in the order given. Use coordinates (x, y), and remember: translations move every point the same way; reflections flip across a line; rotations turn around a stated centre. Show working where you can.

Part A: Follow the sequence

Complete each step in order. A combined transformation means two or more transformations applied one after another.

1.A robot moves a triangle 3 units right, then reflects it in the x-axis. Is this a single transformation or a combined transformation? Explain how you know.

2.Point A starts at (1, 1). Translate it 3 units right and 2 units down. What are its new coordinates?

3.Triangle ABC has vertices A(-3, 1), B(0, 1) and C(-2, 3). First translate every vertex 2 units left and 1 unit up. Then reflect the translated triangle in the x-axis. Write the final coordinates of A, B and C.

4.A point (x, y) is reflected in the y-axis, then translated 2 units up. Which rule gives its final coordinates?

(-x, y + 2)
(x, -y + 2)
(-x, y - 2)
(x + 2, -y)

5.Point P is at (-2, 3). Reflect P in the y-axis, then translate it 4 units down. Give the coordinates after each step and the final coordinates.

Part B: Compare and reason

The order matters. Use coordinates and transformation vocabulary to justify your thinking.

6.Start with Q(1, 2). Compare these sequences: (A) reflect in the y-axis, then translate 3 units right; (B) translate 3 units right, then reflect in the y-axis. Find each final position. Are the results the same?

7.If a point is reflected in the x-axis and then reflected in the y-axis, the final coordinates are (-x, -y). Is this statement true or false? Check it using R(3, -2).

TrueFalse

8.A point at (2, 1) ends at (-1, -2). One possible route is: first move it to (-2, 1), then to (-1, -2). Name a transformation that takes (2, 1) to (-2, 1), and describe the second move as a translation.

9.Grace says point T(4, 2), reflected in the x-axis and then translated 1 unit left, finishes at (3, 2). Find the mistake and give the correct final coordinates.

10.Point S starts at (0, 2) and must finish at (4, -2). Give one sequence using exactly two transformations. State the transformations in order and show the coordinates after each step.