This point will stay in the same position. One corner of the triangle (7,5) is on the mirror line. We can draw the mirror line with a dotted line. The line y = 5 is the line that joins all the points where y is 5. You can see that each point and its corresponding point on the reflected shape are the same distance away from the mirror line.Įxample: Reflect shape A in the line y = 5

The mirror line is shown by the dotted line. Here we have a shape reflected over a mirror line. When a shape is reflected it is flipped over the mirror line.Īfter a shape is reflected each new point is the same distance from the mirror line as the original point.

For a reflection we need a line of reflection (a mirror line). We have a rotation, 90° anticlockwise, about the centre (3,2)Ī reflection is a mirror image of a shape. If we hold the tracing paper at (3,2) and rotate the paper we will see that the arrow is facing left when the triangle is on shape B. If the tracing paper is held at (3,2) shape A should spin onto shape B.Īt (3,2) on the tracing paper we can draw an arrow facing up We then have to work out where to hold the tracing paper (the bit of the paper that is kept in the same position when the paper is rotated). To do this we get a piece of tracing paper and draw around the shape (shape A). We can use tracing paper to help work this out. To describe the transformation we also need to know the centre of rotation and how far the shape has turned (the angle) Here the shape has been turned, we have a rotation. To finish we need to draw the rotated shape on the paperĮxample: Describe the transformation that maps shape A onto shape B. When the tracing paper has spun 180° the arrow will be facing down We now need to hold the tracing paper at the centre of rotation (you can hold a pencil on the centre of rotation) and spin the tracing paper around 180° We can also add an arrow pointing up from the centre of rotation On the tracing paper we draw around the shape and mark the centre of rotation We can use tracing paper to rotate a shape The fixed point is called the centre of rotation.Įxample: Rotate shape A 180° about centre (1,1) We can now move this point 5 right and then 2 up.įrom this point we need to draw a shape that is the same as shape A.Ī rotation turns a shape around a fixed point. We can start by picking a point on shape A. Means we need to move the shape 5 right and 2 up The transformation is a translation by the vector We can write 6 left and 5 up as a vector:

We have a translation 6 to the left and 5 up. Next we look at how far to move in the up or down direction: We can now look at how far we need to move to get from the point on A to the same point on Bįirstly we look at the left or right direction: To find out how much the shape has moved we need to pick a point on shape A and find the same point on shape B. We put a set of brackets around these numbers.Ī movement to the right is positive and a movement to the left is negative.Ī movement up is positive and a movement down is negative. We write the left/right movement on top of the up/down movement. We can describe a translation using a vector.

The transformation that maps shape A onto shape B is a translation 4 right and 3 up. Now we can look at how far up or down to move. We start by looking at how far to move left or right. If we take the bottom right corner of A we have to see how far we have to move the to get to the bottom right corner of B. We need to know how far to move left/right and how far to move up/down. We can take any point of shape A and see how far we have to move to get to the same point on shape B. We also need to know by how much the shape has moved. This transformation is called a translation We can see that the shape has moved and all points have moved by the same amount. All points of the shape must be moved by the same amount.Ī translation can be up or down and left or right.Įxample: Describe the transformation that maps shape A onto shape B

Rotation rules in geometry