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 Gets us to point A.A translation moves a shape. That and it looks like it is getting us right to point A. Our center of rotation, this is our point P, and we're rotating by negative 90 degrees. Which point is the image of P? So once again, pause this video and try to think about it. Than 60 degree rotation, so I won't go with that one. And it looks like it's the same distance from the origin. ![]() Like 1/3 of 180 degrees, 60 degrees, it gets us to point C. So does this look like 1/3 of 180 degrees? Remember, 180 degrees wouldīe almost a full line. One way to think about 60 degrees, is that that's 1/3 of 180 degrees. So this looks like aboutĦ0 degrees right over here. P is right over here and we're rotating by positive 60 degrees, so that means we go counterĬlockwise by 60 degrees. It's being rotated around the origin (0,0) by 60 degrees. Which point is the image of P? Pause this video and see That point P was rotated about the origin (0,0) by 60 degrees. I included some other materials so you can also check it out. There are many different explains, but above is what I searched for and I believe should be the answer to your question. There is also a system where positive degree is clockwise and negative degree anti-clockwise, but it isn't widely used. Product of unit vector in X direction with that in the Y direction has to be the unit vector in the Z direction (coming towards us from the origin). ![]() Clockwise for negative degree.įor your second question, it is mainly a conventional that mathematicians determined a long time ago for easier calculation in various aspects such as vectors.
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