GraphicMaths

Visualising maths

Clockwise rotations

In this example, we will look at clockwise rotations, where the centre of rotation is the origin. To see the effect in the interactive diagram below, click one of the buttons to rotate by 90°, 180° or 270°. You must click the reset button to return the shape to its original position before trying another angle. If you wish, you can also move the shape to different position, by dragging the red point in the centre of the shape. Read more →

Anticlockwise rotations

In this example, we will look at anticlockwise rotations, where the centre of rotation is the origin. To see the effect in the interactive diagram below, click one of the buttons to rotate by 90°, 180° or 270°. You must click the reset button to return the shape to its original position before trying another angle. If you wish, you can also move the shape to different position, by dragging the red point in the centre of the shape. Read more →

Rotations

Rotation spins a shape around a particular point, called the centre of rotation. To describe a rotation, you need to give three things: the angle of rotation, for example 90° the direction of rotation (clockwise or anticlockwise) the centre of rotation For the simple examples here, we will always rotate shapes around the origin. Read more →

Horizontal translation

Translation is specified a a vector (x, y), where x is the distance moved is the horizontal direction and y is the distance moved in the vertical direction. For horizontal movement, the y value is zero. A positive x moves the shape to the right, negative moves it to the left. In the diagram below, click the button labelled (5, 0) to move the shape 5 units to the right. Then press the reset button to set it back to its original position. Read more →

Translations

A translation moves a shape to a different position. The shape can move horizontally, or vertically, or both. Translation is specified a a vector (x, y), where x is the distance moved is the horizontal direction and y is the distance moved in the vertical direction. To describe a translation, you must give the number of units the shape is translated in the x and y directions. Read more →

Translations in any direction

You can translate a shape horizontally and vertically at the same time, which will cause the shape to move to a different x and y position. You do this using a vector with both x and y values. In this diagram, you can translate the shape by: the vector (-7, 2), moving the shape left by 7 units and up by 2. the vector (1, -5), moving the shape right by 1 unit and down by 5. Read more →

Vertical translation

For vertical movement, the x value is zero. A positive y moves the shape up, negative moves it down. In the diagram below, click the button labelled (0, 5) to move the shape up by 5 units. Again, press the reset button to set it back to its original position. Then try clicking the button labelled (0, -4) to move the shape down by 3 units. Read more →