Examples, solutions, videos to help GCSE Maths students learn about different types of Transformation: Translation, Reflection, Rotation and Enlargement.

The following figures show the four types of transformations: Translation, Reflection, Rotation, and Enlargement. Scroll down the page for more examples and solutions using the transformations.

This video shows how to transform a shape using a given translation vector.

Examples:

1. Plot the points (1,1), (2,1) and (1,2) and connect the dots to make a polygon.

Label your shape A and carry out the transformation. Translate A by the given vector and label the shape B.

2. State fully the single transformation that maps A to B.

Understand simply how to reflect shapes in vertical and horizontal lines. The trick is in understanding the equations of the horizontal and vertical lines. Reflections to help with GCSE mathematics, one in a line of the form x = a another in a line of the form y = b.

Example:

(a) Reflect shape A in the x-axis and label it shape B.

(b) Reflect shape A in the y-axis and label it shape C.

(c) Reflect shape A in the line x = 3 and label it shape D.

(d) Reflect shape A in the line y = 3 and label it shape E.

(e) Reflect shape A in the line y = -0.5 and label it shape F.

(f) Reflect shape A in the line y = x and label it shape G.

(g) Reflect shape A in the line y = -x and label it shape H.

Rotating a polygon around the origin.

For a 90-degree rotation around the origin, switch the x,y values of each ordered pair for the location of the new point.

Example:

Rotate ABC about (0,-1) by 90° clockwise.

GCSE mathematics revision help. An example on how to enlarge a shape by a positive and negative scale factor for GCSE revision. A scale factor of 2 and -2 is chosen.

GCSE Maths revision Exam paper practice & help.

Example:

Triangle PQR is shown on the grid.

(a) Enlarge triangle PQR by scale factor 1/3 with centre of enlargement C(4,5)

(b) Triangle PQR is enlarged by scale factor -3 with centre of enlargement C(4,5). P is mapped onto (31,14). Calculte the coordinated of the point that Q is mapped onto.

Reflection, rotation and enlargement from GCSE mathematics, foundation level.

Examples:

(a) Enlarge triangle T by scale factor 3, centre the origin. Label the image A.

(b) Rotate the triangle T through 90° anti-clockwise anout the origin. Label the image B.

(c) Reflect triangle I in the line x = 4. Label the image C.

GCSE Math AQA Q6 Higher Paper 1 June 2007

Example:

The diagram shows two triangles, A and B.

(a) Describe fully the single transformation that maps triangle A onto triangle B.

(b) On the diagram, draw an image of triangle after it is reflected in the line y = x. Label your image C.

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