Under a rotation about the indicated turn center. If you get stuck, review the examples in the lesson, then try again.ġ) In the diagrams, the purple flag is the image of the green one Now get a pencil, an eraser and a note book (graph paper), copy the questions,ĭo the practice exercise(s),then check your work with the solutions. And that's why we don't switch the coordinates, we just change both signs. So, we can see that a rotation of 180° in either direction can be described as 2 consecutive reflections - one vertical, one horizontal. When we inspect the relative positions of the green and blue triangles, the ones resulting from a turn of 180°, we see that we would get the same result if we had reflected the green triangle first in the x-axis and then in the y-axis. Let's take another look at the first diagram.Ī Rotation changes the ORIENTATION of a figure. Rotations about the Origin of 180° and 270° Solution: we must switch the coordinates and change the sign of the y-value (after the switch!!) because it is a clockwise rotation. Find the coordinates of the image vertices if quadrilateral ABCD is rotated 90° clockwise about the origin.
Had our figure started out, below the axis, it would've ended up above it, so again, the sign of the second coordinate - y - will change.Įxample: A(2, 0) B(6, 3) C(6, 6) D(2, 3). The reason the y-value changes sign is that we move the figure from above the x-axis to below it. Notice also how under a clockwise rotation of 90° about the origin:
Had our figure started out left of the axis, it would've ended up on the right side, so again, the sign of the first coordinate - x - has to change. The reason the x-value changes sign is that under a counterclockwise rotation, we move the figure from right of the y-axis to left of it. Since 0 is neither positive nor negative, we don't see the change in sign, however, in point A we can see it. Notice how under a counterclockwise rotation of 90° about the origin: Let's look at the changes in a figure's vertex coordinates under rotations of 90°, both counterclockwise and clockwise. Rotations about the Origin: (multiples of 90°) Though we can rotate any two dimensional figure about any point in the plane through any angle, we usually begin our study of rotations with multiples of 90° about the origin. Notice how we define a rotation with 3 pieces of information: The big (minute) hand turns through 360° every hour, the little (hour) hand rotates 1/12 of that or 30° every hour whereas the second hand races around doing a 360° turn every minute! The hands of a clock rotate clockwise (of course!) about the center of the clock's face as time passes. The degree measure of the turn is called the angle of rotation. In the plane by turning it about a point called the center of rotation. In geometry, a rotation is a transformation that changes the position of a figure Rotations about the origin ROTATIONS ABOUT THE ORIGIN