7.7 The student will apply translations and reflections of right triangles or rectangles in the coordinate plane. Understanding the Standard Essential Knowledge and Skills The student will use problem solving, mathematical A transformation of a figure called the preimage changes the size, shape, or position of the figure to communication, mathematical reasoning, connections, and a new figure called the image. representations to Translations and reflections do not change the size or shape of a figure (e.g., the preimage and Given a preimage in the coordinate plane, identify the image are congruent figures). Translations and reflections change the position of a figure. coordinates of the image of a right triangle or rectangle that has A translation is a transformation in which an image is formed by moving every point on the been translated either vertically, horizontally, or a combination preimage the same distance in the same direction. of a vertical and horizontal translation. A reflection is a transformation in which an image is formed by reflecting the preimage over a line Given a preimage in the coordinate plane, identify the called the line of reflection. All corresponding points in the image and preimage are equidistant coordinates of the image of a right triangle or a rectangle that has from the line of reflection. been reflected over the or x- y-axis. The image of a polygon is the resulting polygon after the transformation. The preimage is the Given a preimage in the coordinate plane, identify the polygon before the transformation. coordinates of the image of a right triangle or rectangle that has been translated and reflected over the or or reflected x- y-axis A transformation of preimage point can be denoted as the image (read as A Aʹ “A prime”). over the or and then translated. x- y-axis The preimage of a figure that has been translated and then reflected over the or may result x- y-axis Sketch the image of a right triangle or rectangle that has been in a different transformation than the preimage of a figure that has been reflected over the or x- translated vertically, horizontally, or a combination of both. and then translated. Sketch the image of a right triangle or rectangle that has been reflected over the or x- y-axis. Sketch the image of a right triangle or rectangle that has been translated and reflected over the or or reflected over the x- y-axis or and then translated. x- y-axis
7.7 The student will apply translations and reflections of right triangles or rectangles in the coordinate plane. Understanding the Standard Essential Knowledge and Skills A transformation of a figure called the preimage changes the size, shape, or position of the figure to a new figure called the image. Translations and reflections do not change the size or shape of a figure (e.g., the preimage and image are congruent figures). Translations and reflections change the position of a figure. A translation is a transformation in which an image is formed by moving every point on the preimage the same distance in the same direction. A reflection is a transformation in which an image is formed by reflecting the preimage over a line called the line of reflection. All corresponding points in the image and preimage are equidistant from the line of reflection. The image of a polygon is the resulting polygon after the transformation. The preimage is the polygon before the transformation. A transformation of preimage point A can be denoted as the image Aʹ (read as “A prime”). The preimage of a figure that has been translated and then reflected over the x- or y-axis may result in a different transformation than the preimage of a figure that has been reflected over the x- or and then translated. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Given a preimage in the coordinate plane, identify the coordinates of the image of a right triangle or rectangle that has been translated either vertically, horizontally, or a combination of a vertical and horizontal translation. Given a preimage in the coordinate plane, identify the coordinates of the image of a right triangle or a rectangle that has been reflected over the x- or y-axis. Given a preimage in the coordinate plane, identify the coordinates of the image of a right triangle or rectangle that has been translated and reflected over the x- or y-axis or reflected over the x- or y-axis and then translated. Sketch the image of a right triangle or rectangle that has been translated vertically, horizontally, or a combination of both. Sketch the image of a right triangle or rectangle that has been reflected over the x- or y-axis. Sketch the image of a right triangle or rectangle that has been translated and reflected over the x- or y-axis or reflected over the x- or y-axis and then translated.
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