Transformations Day 1 Notes Slideshow

Translation Notes A translation, or shift, is a transformation that moves each point of a figure the same distance in the same direction. Horizontal Translation In a horizontal translation the x-coordinate moves, but the y-coordinate stays the same. A horizontal translation of a units can be represented by the function (x ± a, y) If a is greater than 0 the figure slides to the right If a is less than 0 the figure slides left Vertical Translation In a vertical translation the y-coordinate moves, but the x-coordinate stays the same. A vertical translation of b units can be represented by the function (x, y ± b) If b is greater than 0 the figure slides up If b is less than 0 the figure slides down

Reflection Notes A reflection is a transformation that flips a figure across a line called a line of reflection Each reflected point is the same distance from the line of reflection as the corresponding point on the pre-image, but on the opposite side of the line. So, the resulting image and the preimage are mirror images of one another. The line of reflection can be the x-axis, y-axis, or any other line in the coordinate plane. The 6 most common lines of reflection are: x-axis (x, y)  (x, -y) y-axis (x, y)  (-x, y) x = a (x, y)  (x ± distance to a, y) y = b (x, y)  (x, y ± distance to b) y = x (x, y)  (y, x) y = -x (x, y)  (-y, -x)

Rotation Notes A rotation is a transformation that turns a figure around a point called the center of rotation. Remember that a circle is the set of all points that are the same distance from a point called the center. When you rotate a point around a center of rotation, it remains the same distance from the center of rotation, just like a circle. So a rotation is when al the points in the pre-image are moved along circular arcs determined by the center of rotation and the angle of rotation. When you are asked to rotate a figure, you must remember each of the following: Center of Rotation Angle of Rotation Direction of Rotation – Counterclockwise by default

Translation Notes A translation, or shift, is a transformation that moves each point of a figure the same distance in the same direction. Horizontal Translation In a horizontal translation the x-coordinate moves, but the y-coordinate stays the same. A horizontal translation of a units can be represented by the function (x ± a, y) If a is greater than 0 the figure slides to the right If a is less than 0 the figure slides left Vertical Translation In a vertical translation the y-coordinate moves, but the x-coordinate stays the same. A vertical translation of b units can be represented by the function (x, y ± b) If b is greater than 0 the figure slides up If b is less than 0 the figure slides down

Reflection Notes A reflection is a transformation that flips a figure across a line called a line of reflection Each reflected point is the same distance from the line of reflection as the corresponding point on the pre-image, but on the opposite side of the line. So, the resulting image and the preimage are mirror images of one another. The line of reflection can be the x-axis, y-axis, or any other line in the coordinate plane. The 6 most common lines of reflection are: x-axis (x, y)  (x, -y) y-axis (x, y)  (-x, y) x = a (x, y)  (x ± distance to a, y) y = b (x, y)  (x, y ± distance to b) y = x (x, y)  (y, x) y = -x (x, y)  (-y, -x)

Rotation Notes A rotation is a transformation that turns a figure around a point called the center of rotation. Remember that a circle is the set of all points that are the same distance from a point called the center. When you rotate a point around a center of rotation, it remains the same distance from the center of rotation, just like a circle. So a rotation is when al the points in the pre-image are moved along circular arcs determined by the center of rotation and the angle of rotation. When you are asked to rotate a figure, you must remember each of the following: Center of Rotation Angle of Rotation Direction of Rotation – Counterclockwise by default