3/30/2024 0 Comments Rotations rules in geometry![]() 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 In many cases, a translation will be both horizontal and vertical, resulting in a diagonal slide across the coordinate plane.A translation moves a shape. Negative values equal vertical translations downward. Positive values equal vertical translations upward. Negative values equal horizontal translations from right to left.Ī vertical translation refers to a slide up or down along the y-axis (the vertical access). Positive values equal horizontal translations from left to right. Vertical TranslationsĪ horizontal translation refers to a slide from left to right or vice versa along the x-axis (the horizontal access). Geometry Dilations Explained: Free Guide with Examples Geometry Reflections Explained: Free Guide with Examples Geometry Rotations Explained: Free Guide with Examples ![]() To learn more about the other types of geometry transformations, click the links below: Note that a translation is not the same as other geometry transformations including rotations, reflections, and dilations. A translation is a slide from one location to another, without any change in size or orientation.
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