Geometric Transformations
A rotation means to turn around a corner. The distance from the the center (point of orgin) to any point on the shape stays the same. Every point makes a circle around the center.
To rotate an object you need a center of rotation and how much you want to rotate it. By convention, positive rotations go counter clockwise, and negative rotations go clockwise.
Rotations - Turning Around a Circle A rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation.
Steps in performing a rotation:
1) CIRCLES: Use your compass to create circles from the point of orgin (center) through all corners of the shape in which you are about to rotate.
2) LINES: Draw lines connecting the point of orgin through all corners of the shape, through all the circles.
3) MEASURE: Use your protractor to measure the angle (amount of degrees) in which you want to rotate.
4) CREATE: Connect the dots and create your new shape.
In geometry, translation simply means: moving without rotating, resizing or anything else. JUST MOVING! To translate a shape, every point of the shape must move the same distance in the same direction.
Steps in performing a translation:
1) MEASURE: Use your ruler to measure the (guide line) distance in which you are required to move the image. The direction of the arrow will also determine the the angle in which you are to move this image.
2) CREATE DOTTED GUIDE LINES: Use your triangle shaped ruler to create perpendicular dotted lines connecting the GUIDE LINE and each corner of the original shape.
3) CREATE NEW POINTS: Use the dotted lines to maintain the angle in which you are to move/translate this image. Use a ruler to measure the distance in which you want to move the image and create new points.
4) CONNECT: Create new image by connecting the dots.
A reflection is a transformation that flips a figure accross a line. The Line of Symmetry (also called the Mirror Line) does not have to be up-down or left-right, it can be in any direction. In geometry, a transformation that reflects every point on a shape to a point that is the same distance on the opposite side of a fixed line – the mirror line, or line of symmetry.
Steps in performing a reflection:
1) CREATE DOTTED GUIDE LINES: Use your triangle shaped ruler to create perpendicular dotted lines connecting the MIRROR LINE and each corner of the shape.
2) EXTEND: Now extend those lines an equal distance on the opposite side of the GUIDE LINE (Mirror line).
3) MEASURE: Measure the distance between the mirror line and the corners of the image. Now, measure an equal distance on the other side of the mirror line.
4) CONNECT: Create new image by connecting the dots.
A transfomation is also known as RESIZING an image (also calleddilation, contraction, compression, enlargement or even expansion). The shape becomes bigger or smaller, but still looks similar: all angles are the same and image is still proportional. (Note: You will be given a Ratio of Similitude = K)
Steps in performing a transformation:
1) CREATE DOTTED GUIDE LINES: Use a ruler to created dotted guide lines through each corner from the point of origin.
2) MEASURE: Measure the distance from each corner point to the point of origin.
3) USE RATIO OF SIMILITUDE (K): Multiply the distance from each point by the K and create new point.
4) CONNECT: Create new image by connecting the dots.
A rotation means to turn around a corner. The distance from the the center (point of orgin) to any point on the shape stays the same. Every point makes a circle around the center.
To rotate an object you need a center of rotation and how much you want to rotate it. By convention, positive rotations go counter clockwise, and negative rotations go clockwise.
- "Center" is the 'center of rotation.' This is the point around which you are performing your mathematical rotation.
- "Degrees" stands for how many degrees you should rotate. A positive number usually by convention means counter clockwise.
Rotations - Turning Around a Circle A rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation.
Steps in performing a rotation:
1) CIRCLES: Use your compass to create circles from the point of orgin (center) through all corners of the shape in which you are about to rotate.
2) LINES: Draw lines connecting the point of orgin through all corners of the shape, through all the circles.
3) MEASURE: Use your protractor to measure the angle (amount of degrees) in which you want to rotate.
4) CREATE: Connect the dots and create your new shape.
In geometry, translation simply means: moving without rotating, resizing or anything else. JUST MOVING! To translate a shape, every point of the shape must move the same distance in the same direction.
Steps in performing a translation:
1) MEASURE: Use your ruler to measure the (guide line) distance in which you are required to move the image. The direction of the arrow will also determine the the angle in which you are to move this image.
2) CREATE DOTTED GUIDE LINES: Use your triangle shaped ruler to create perpendicular dotted lines connecting the GUIDE LINE and each corner of the original shape.
3) CREATE NEW POINTS: Use the dotted lines to maintain the angle in which you are to move/translate this image. Use a ruler to measure the distance in which you want to move the image and create new points.
4) CONNECT: Create new image by connecting the dots.
A reflection is a transformation that flips a figure accross a line. The Line of Symmetry (also called the Mirror Line) does not have to be up-down or left-right, it can be in any direction. In geometry, a transformation that reflects every point on a shape to a point that is the same distance on the opposite side of a fixed line – the mirror line, or line of symmetry.
Steps in performing a reflection:
1) CREATE DOTTED GUIDE LINES: Use your triangle shaped ruler to create perpendicular dotted lines connecting the MIRROR LINE and each corner of the shape.
2) EXTEND: Now extend those lines an equal distance on the opposite side of the GUIDE LINE (Mirror line).
3) MEASURE: Measure the distance between the mirror line and the corners of the image. Now, measure an equal distance on the other side of the mirror line.
4) CONNECT: Create new image by connecting the dots.
A transfomation is also known as RESIZING an image (also calleddilation, contraction, compression, enlargement or even expansion). The shape becomes bigger or smaller, but still looks similar: all angles are the same and image is still proportional. (Note: You will be given a Ratio of Similitude = K)
Steps in performing a transformation:
1) CREATE DOTTED GUIDE LINES: Use a ruler to created dotted guide lines through each corner from the point of origin.
2) MEASURE: Measure the distance from each corner point to the point of origin.
3) USE RATIO OF SIMILITUDE (K): Multiply the distance from each point by the K and create new point.
4) CONNECT: Create new image by connecting the dots.