Some geometry lessons will connect back to algebra by describing the formula causing the translation. That's what makes the rotation a rotation of 90°. Also all the colored lines form 90° angles. Notice that all of the colored lines are the same distance from the center or rotation than than are from the point. The figure shown at the right is a rotation of 90° rotated around the center of rotation. Also, rotations are done counterclockwise! You can rotate your object at any degree measure, but 90° and 180° are two of the most common. Reflection over line y = x: T( x, y) = ( y, x)Ī rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation. Reflection over y-axis: T(x, y) = (- x, y) Reflection over x-axis: T( x, y) = ( x, - y) In other words, the line of reflection is directly in the middle of both points.Įxamples of transformation geometry in the coordinate plane. The line of reflection is equidistant from both red points, blue points, and green points. Notice the colored vertices for each of the triangles. Let's look at two very common reflections: a horizontal reflection and a vertical reflection. The transformation for this example would be T( x, y) = ( x+5, y+3).Ī reflection is a "flip" of an object over a line. More advanced transformation geometry is done on the coordinate plane. In this case, the rule is "5 to the right and 3 up." You can also translate a pre-image to the left, down, or any combination of two of the four directions. The formal definition of a translation is "every point of the pre-image is moved the same distance in the same direction to form the image." Take a look at the picture below for some clarification.Įach translation follows a rule. The most basic transformation is the translation. Translations - Each Point is Moved the Same Way This resource does a good job of focusing on the distance and angle preservation of rigid motions.The original figure is called the pre-image the new (copied) picture is called the image of the transformation.Ī rigid transformation is one in which the pre-image and the image both have the exact same size and shape. Only ask questions about translations and reflections, not rotations. This resource does a good job of focusing on the distance preservation of rigid motions. This Mathematics Assessment Project lesson will be used in the next unit, but can be used as a reference for style to create matching cards for this lesson. Include matching cards with lines of reflection, original figures, and final figures.Translate angles and segments as review.Reflect a line segment given the line of reflection.Describe a reflection with algebraic notation (if an axis or y=x /y=-x line).Reflect an angle given the line of reflection.Find the line of reflection, citing half the distance between corresponding points on the two line segments.Include problems where students need to:.Describe the relationship between the distance of each point on the original figure and the reflected figure to the line of reflection.Understand that there are an infinite number of fixed points with a reflection, but all fixed points are on the line of reflection.Describe where the general rule is derived from. Use an algebraic rule to show the reflection of a figure over an axis or the line y=x.Perform a reflection on a coordinate plane by reflecting points over any given line (not just an axis or y=x).Describe that a line of reflection can be in any orientation (horizontal, vertical, or diagonal) and that it can be on a figure, outside a figure, intersect with a figure, or be inside a geometric figure.To define a reflection, all that is needed is a line of reflection. Describe reflections as a rigid motion of individual points across a line of reflection.Describe that rigid motions describe ways you can move a figure either on or off a coordinate plane without changing size, shape, angles, or relationship between any of the parts.
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