![]() ![]() Step 3: Draw both shapes by joining their corresponding vertices together with straight lines. Step 2: Plot the vertices of the original and reflected images on the coordinate plane. The new set of vertices will correspond to the vertices of the reflected image. Step 1: Following the reflection rule for this case, change the sign of the x-coordinates of each vertex of the shape, by multiplying them by \(-1\). The steps to follow to perform a reflection over the y-axis are as pretty much the same as the steps for reflection over the x-axis, but the difference is based of the on the change in the reflection rule. The y-coordinates of the vertices will remain the same.The x-coordinates of the vertices that form part of the shape will change sign.Step 3 The new brick is in place.The rule for reflecting over the y-axis is as follows: Type of Reflection Step 2 The brick is then rotated 90° counterclockwise about point M, given here. Step 1A brick is copied and translated to the right one brick length. LANDSCAPING Describe the transformations that are combined to create the brick pattern shown. Graph ΔTUV and its image after a translation along –1, 5 and a rotation 180° about the origin. Graph Other Compositions of Isometries ΔTUV has vertices T(2, –1), U(5, –2), and V(3, –4). Reflections over two intersection lines equals One rotation Answer:EFGH is transformed onto E''F''G''H'' by a translation down a distance that is twice the distance between lines p and q. ![]() Then describe a single transformation that maps EFGH onto E''F''G''H''. Reflections over two parallel lines equals One translationĬopy and reflect figure EFGH in line p and then line q. Two rotations, same center equal One rotation Glide reflections, reflections, translations, and rotations are the only four rigid motions or isometries in a plane. 652 The composition of two or more isometries – reflections, translations, or rotations results in an image that is congruent to its preimage. Translations, reflections and rotations are isometries. Which point is located at (–3, 0)? A.R' B.S' C.T' D.U'ĭefinition An isometry is a transformation that preserves distance. Graph RSTU and its image after a translation along –4, 1and a reflection in the x-axis. Graph BGTS and its image after a translation along 5, 0 and a reflection in the x-axis. It changes one image into another.ĭefinition When a transformation is applied to a figure, and then another transformation is applied to its image, the result is called a composition of the transformations.įind a single transformation for a 75° counterclockwise rotation with center (2,1) followed by a 38° counterclockwise rotation with center (2,1) 113° counterclockwise rotation with center (2,1) 38° 75°įind a single transformation equivalent to a translation with vector followed by a translation with vector. Morphing Morphing is a popular special effect in movies. Draw compositions of reflections in parallel and intersecting lines.Ĭomposite Photograph Composite photographs are made by superimposing one or more photographs.Draw glide reflections and other compositions of isometries in the coordinate plane.9-4 Compositions of Transformations You drew reflections, translations, and rotations.
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