What happens when you rotate a point 90 degrees?
What happens when you rotate a point 90 degrees?
90 Degree Rotation When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
How do you tell if a shape has been rotated?
A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction. You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.
How do you know if a shape is rotation clockwise or counterclockwise?
Rotations may be clockwise or counterclockwise. When working in the coordinate plane: assume the center of rotation to be the origin unless told otherwise. assume a positive angle of rotation turns the figure counterclockwise, and a negative angle turns the figure clockwise (unless told otherwise).
What is the rule for 180 degree rotation?
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
Why do two reflections rotate?
The composition of reflections over two intersecting lines is equivalent to a rotation. The double reflections are equivalent to a rotation of the pre-image about point P of an angle of rotation which is twice the angle formed between the intersecting lines (theta).
Can any translation be replaced by 2 rotations?
One way to replace a translation with two reflections is to first use a reflection to transform one vertex of the pre-image onto the corresponding vertex of the image, and then to use a second reflection to transform another vertex onto the image. Any translation can be replaced by two rotations.
Are two reflections a rotation?
The composition of two reflections across intersecting lines is equivalent to a rotation.
What are the two reflections?
Two reflections over intersecting lines. Reflecting over two intersecting lines is the same as a rotation. Use this diagram to compare the angle of rotation with the angle of intersection of the lines of reflection. 1.
Can reflections intersect?
Compositions of Reflections in Intersecting Lines The compositions of reflections over intersecting lines theorem states that if we perform a composition of two reflections over two lines that intersect, the result is equivalent to a single rotation transformation of the original object.
What happens when you reflect a pair of parallel lines?
This video shows how reflecting a figure in a line and then reflecting the image in a parallel line has the same result as translating the figure in a direction perpendicular to the reflection lines for a distance equal to twice the distance between the lines. …
How do you change parallel lines?
Therefore, a translation or a reflection are possible transformations to create parallel lines. If a reflection is used, the line of reflection has to be parallel with the given line. The last rigid motion, a rotation, can not be used to create parallel lines since it changes the direction of the line.
What happens when you reflect a figure over two non parallel lines?
Test it for yourself by drawing any shape and any two lines with the same slope. Parallel diagonal lines will translate a shape diagonally, horizontal lines will move a translate up and down, and vertical lines will translate a shape left and right. Reflecting over two intersecting lines would create a rotation.
Why do translations produce parallel lines?
The distance between the lines stays constant, and they never intersect. In other words, you can translate (move) either line by that constant distance, in some direction, to get the other line. It’s just like how when you change the y-intercept but keep the slope the same, you get parallel lines.
What is the original figure in a transformation called?
Pre-Image
What are two figures with the same shape but different sizes called?
Two figures are congruent if they have the same shape and size. Two angles are congruent if they have the same measure. Although they are the same shape, they are different sizes. Figures that are the same shape but different in size are similar.
What is a transformation that turns a figure?
rotation