6 Reflections-(Flip)When you reflect a shape in the coordinate plane, you reflect it over a line. This line is called the line of reflection/symmetry.When a figure is reflected on a coordinate plane, every point of the figure must have a corresponding point on the other side.
7 Most reflections are over the x-axis (horizontal), the y-axis (vertical), or the line y = x (diagonal uphill from left to right.)
8 ReflectionsWhen you reflect a shape over the x –axis, use the same coordinates and multiply the y coordinate by –1. (x, opposite y)When you reflect a shape over the y-axis, use the same coordinates and multiply the x coordinate by –1. (opposite x, y)When you reflect a shape over the line y=x, use the same coordinates and multiply both by –1.
9 Examples:1. Reflect the triangle over the x-axis and y – axis.
12 Translations (Slides/Glide) To translate a figure in the direction describe by an ordered pair, add the ordered pair to the coordinates of each vertex of the figure.The new set of ordered pairs is called the image. It is shown by writing A’. This is read the image of point A.
13 ExamplesFind the coordinates of the vertices of each figure after the translation described. Use the graph to help you.
14 Examples:Find the coordinates of the vertices of each figure after the translation described.
16 90 degrees rotation moves 1 quadrant In the coordinate plane we have 4 quadrants. If the shape is rotated around (0,0) then:90 degrees rotation moves 1 quadrantRotating 90 clockwise. (x, y) (y, opposite x)same as 270 counterclockwise.Rotating 90 counterclockwise is thesame as 270 clockwise. (x, y) (opposite y, x)180 degrees rotation moves 2 quadrantsMultiply both by – 1.(x, y,) (opposite x, opposite y)270 degrees rotation moves 3 quadrantsRotating 270 counterclockwise is the same as 90 clockwise(x, y) (y, opposite x)360 degrees rotation moves 4 quadrants(stays the same)
17 Examples:If a triangle is in Quadrant 2 and is rotated 270 counterclockwise, what quadrant is it now in?If a triangle is in Quadrant 4 and is rotated 90 clockwise, what quadrant is it now in?
18 SymmetryTwo Types:1. Line Symmetry (can be called reflectional symmetry)– if you can fold a shape and have the edges meetThe place where you fold is called the line of symmetry
25 Examples:Do the following shapes have line symmetry? If so, how many lines of symmetry do they have?a b c d e.
26 Rotational Symmetry2. Rotational Symmetry: If you can turn the shape less than 360o and still have the same shape.Order of Rotational Symmetry: Is the number of rotations that must be made to return to the original orientationMinimum Rotational Symmetry: The smallest number of degrees a shape can be rotated and fit exactly on itselfHint: Take 360o divided by the number of sides/points.