You can know how to slide a shape using the T ( a, b ) T ( − 10, 3 ) because the first value is always the x-axis. To avoid confusion, the new image is indicated with a little prime stroke, like this: P′, and that point is pronounced “ P prime. Suppose you have Point P located at (3, 4). The original reference point for any figure or shape is presented with its coordinates, using the x-axis and y-axis system, (x,y). Reflection – exchanging all points of a shape or figure with their mirror image across a given line (like looking in a mirror) Stretch – a one-way or two-way change using an invariant line and a scale factor (as if the shape were rubber) Shear – a movement of all the shape’s points in one direction except for points on a given line (like a crate being collapsed) Rotation – turning the object around a given fixed pointĭilation – a decrease in scale (like a photocopy shrinkage)Įxpansion – an increase in scale (like a photocopy enlargement) Translation – moving the shape without any other change You can perform seven types of transformations on any shape or figure: Translations are the simplest transformation in geometry and are often the first step in performing other transformations on a figure or shape.įor example, you may find you want to translate and rotate a shape. an isometry) because it does not change the size or shape of the original figure. And so this would be negative 90 degrees, definitely feel good about that.A translation is a rigid transformation (a.k.a. And this looks like a right angle, definitely more like a rightĪngle than a 60-degree angle. And once again, we are moving clockwise, so it's a negative rotation.
This is where D is, and this is where D-prime is. Point and feel good that that also meets that negative 90 degrees. This looks like a right angle, so I feel good about We are going clockwise, so it's going to be a negative rotation. Too close to, I'll use black, so we're going from B toī-prime right over here. Let me do a new color here, just 'cause this color is Much did I have to rotate it? I could do B to B-prime, although this might beĪ little bit too close. I can take some initial pointĪnd then look at its image and think about, well, how I don't have a coordinate plane here, but it's the same notion. Well, I'm gonna tackle this the same way. So once again, pause this video, and see if you can figure it out. So we are told quadrilateral A-prime, B-prime, C-prime,ĭ-prime, in red here, is the image of quadrilateralĪBCD, in blue here, under rotation about point Q. So just looking at A toĪ-prime makes me feel good that this was a 60-degree rotation. And if you do that with any of the points, you would see a similar thing. Another way to thinkĪbout is that 60 degrees is 1/3 of 180 degrees, which this also looks
Like 2/3 of a right angle, so I'll go with 60 degrees. One, 60 degrees wouldīe 2/3 of a right angle, while 30 degrees wouldīe 1/3 of a right angle. This 30 degrees or 60 degrees? And there's a bunch of ways The counterclockwise direction, so it's going to have a positive angle. And where does it get rotated to? Well, it gets rotated to right over here. Remember we're rotating about the origin. Points have to be rotated to go from A to A-prime, or B to B-prime, or from C to C-prime? So let's just start with A. So I'm just gonna think about how did each of these So like always, pause this video, see if you can figure it out. Step 1: Note the given information (i.e., angle of rotation, direction, and the rule).If necessary, plot and connect the given points on the coordinate. Like 1/3 of 180 degrees, 60 degrees, it gets us to point C. And it looks like its the same distance from the origin.
We're told that triangle A-prime, B-prime, C-prime, so that's this red triangle over here, is the image of triangle ABC, so that's this blue triangle here, under rotation about the origin, so we're rotating about the origin here. Than 60 degree rotation, so I wont go with that one.