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2D Shape Transformations
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2D Shape Transformations
Solve each task. Unless a question says otherwise, use the coordinate plane with x-values increasing to the right and y-values increasing upwards. Give transformation descriptions precisely, including any required vector, centre, angle, or mirror line.
Identify and describe
Start by identifying how transformations affect shapes.
1.A logo is shifted 5 units left and 2 units up without turning or resizing. Which transformation is this, and what is its vector?
2.A point P is at (4, -3). It is reflected in the y-axis. What are the coordinates of P′?
3.A point Q at (2, 5) is rotated 90° clockwise about the origin. Find Q′. Use the rule (x, y) → (y, -x).
4.Which set of details fully describes a rotation? Choose one.
- A vector only
- A mirror line only
- A centre, an angle, and a direction
- A scale factor only
5.True or false: A reflection preserves side lengths and angle sizes, but reverses the orientation of a shape.
TrueFalse
Track the image
Follow each transformation carefully, applying them in the stated order.
6.Triangle ABC has vertices A(1, 1), B(4, 1), and C(2, 3). It is translated by vector (2, -3). Write the coordinates of A′, B′, and C′.
7.Point R is at (-3, 2). First reflect it in the x-axis, then translate it by vector (4, 1). Find its final coordinates.
8.A rectangle has vertices (1, 1), (5, 1), (5, 3), and (1, 3). It is enlarged by scale factor 2 about the origin. Find the image coordinates of all four vertices.
9.A triangle has an area of 18 cm². It is enlarged by scale factor 3. What is the area of its image? Explain why the area does not simply triple.
Design and justify
Show what you know by constructing and explaining a transformation.
10.On the coordinate plane, draw triangle A(1, 1), B(4, 1), C(2, 3), then draw its image after a 90° anticlockwise rotation about the origin. Label the image vertices A′, B′, and C′.
Draw and label both triangles here.
11.A pattern tile is reflected in the line x = 2. Point S(5, -1) is one of its vertices. Find S′ and explain how you know.
3 printable pages
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