A transformation of a geometric figure is a change in its position, size or shape. When the position of a figure is changed, the original geometric figure (or preimage) is moved on a plane to create an image with the exact same size and shape as the original figure.

A reflection is a transformation in which the original geometric figure (preimage) is flipped over a line, called the line of reflection, to create an image. All corresponding points in the image and the original figure are equidistant (or the same distance) from the line of reflection.

A rotation is a transformation in which the original geometric figure (preimage) is turned about a point in a clockwise or counterclockwise direction to create an image.

A translation is a transformation in which every point of the original figure (preimage) is moved the same distance — up, down, left, or right (a slide).

Given a geometric figure and a transformation of that geometric figure, identify whether the transformation is a reflection (flip), rotation (turn) or translation (slide).

Sample correct answer: The transformation is a reflection over the y-axis or a translation of 9 units left.

Reflect a shape over the x-axis (flip the shape up or down) and identify the coordinates of the vertices of the new shape. When this happens, the x-coordinates remain the same, but the new y-coordinates are opposites of the original.

Reflect a shape over the y-axis (flip the shape left or right) and identify the coordinates of the vertices of the new shape. For this, the y-coordinates remain the same, but the x-coordinates are opposites of the original.

Rotate a shape 90° (around the origin) clockwise or counterclockwise. The new coordinates are determined by first switching the x- and y-coordinates, then taking the opposite of the x- or y-coordinate, depending on the direction of rotation. If the shape is rotated clockwise, take the opposite of the new y-coordinate. If the shape is rotated counterclockwise, take the opposite of the new x-coordinate.

To rotate a shape 180°, switch the x- and y-coordinates and take the opposite of both values.

Translate a figure (in one direction - up/down/left or right) and draw the new figure. Identify the coordinate points of the vertices of the new shape. 'Track' one vertex in the figure and create or determine the shift that the figure has taken. Check with a second vertex that the shift is the same or complete the shift with the remaining vertices.