![]() 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 The four most common reflections are performed over the following lines of reflection: the $x$-axis, the $y$-axis, $y =x$, and $y =-x$.A translation moves a shape. ![]() However, the orientation of the points or vertices changes when reflecting an object over a line of reflection. In fact, in reflection, the angle measures of the objects, parallelism, and side lengths will remain intact. The distances between the vertices of the triangles from the line of reflection will always be the same. The graph above showcases how a pre-image, $\Delta ABC$, is reflected over the horizontal line of reflection $y = 4$. This makes reflection a rigid transformation. When learning about point and triangle reflection, it has been established that when reflecting a pre-image, the resulting image changes position but retains its shape and size. In reflection, the position of the points or object changes with reference to the line of reflection. Once we’ve established their foundations, it will be easier to work on more complex examples of rigid transformations. We’ll explore different examples of reflection, translation and rotation as rigid transformations. It’s time to explore these three examples of basic rigid transformations first. ![]() This makes this transformation a rigid transformation. Rotation: In rotation, the pre-image is “turned” about a given angle and with respect to a reference point, retaining its original shape and size.The image is the result of “sliding” the pre-image but its size and shape remain the same. ![]() Translation: This transformation is a good example of a rigid transformation.Reflection: This transformation highlights the changes in the object’s position but its shape and size remain intact.These three transformations are the most basic rigid transformations there are: Some examples of rigid transformations occur when a pre-image is translated, reflected, rotated or a combination of these three. This is why it’s essential to have a refresher and understand why they’re each classified as a rigid transformation. This shows that when dealing with rigid transformations, it is important to be familiar with the three basic rigid transformations. The series of basic rigid transformations still result in a more complex rigid transformation. The reflected square is then translated $10$ units to the right and $20$ units downward.The reflected points are $5$ units from the left of the vertical line $x = -5$. The square $ABCD$ is reflected over the line $x = -5$.Breaking down the series of transformations performed on the pre-image highlights the story behind the rigid transformation: This shows that the transformation performed on the square is a rigid transformation. Read more How to Find the Volume of the Composite Solid? ![]()
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