Ext 6-8 Sampler

Dilations 50 Grade8 Lesson16, 8ETeacherGuide 52 Objective32: Touse a scale factor tomakedilations of a figure. ELL Materials: XYCoordinatePegboards, rubber bands Vocabulary: scale factor Dilations Onpage51, studentsmade congruent figures by transforming shapes. In this activity, studentswill learn to dilate a figure tomake it largerusing a scale factor of 2. Using anXYCoordinatePegboard, set up the x - y coordinates for four-quadrant plotting. Writeon theboard: Last year, Jimmade a fence aroundhis garden. The fence was 6 feet long and4 feetwide. The corners of the fence were atA (–3, –2); B (–3, 2);C (3, 2); andD (3, –2) Usea rubberband to show Jim’s fenceonyour coordinategrid. Thenext year, Jimwanted to enlargehis garden in the same shapewith a scale factor of 2. The scale factor is the number youuse tomultiply theoriginal dimensions.A scale factor of 2willmakehis fence twice as long and twice aswide as theoriginal fence. Show the fence for the secondyearusingadifferent color rubberband.Are the shapes congruent? (no) Are the shapes similar? (yes) Give thepoints for the cornersofhisnew fence. [A’ (–6, –4); B’ (–6, 4); C’ (6, 4); andD’ (6, –4)] Read the information together at the topof thepage. Ask students togive the coordinates of PointsO, L andD. How shouldwe find the coordinates for thenew figure? (multiply all coordinates by2) Find thenew coordinates forO,MandP. Lookatproblem1.Will thisnew rectanglebe smaller or larger than theoriginal rectangle?Howdoyouknow? (Smaller, because thewholenumbers arebeingmultiplied by a fraction.) X Y Have students first find the coordinates of the4points from the grid [A (0, 0); B (6, 0); C (6, 3);D (0, 3)] Multiply the coordinatesby⅓.Write the coordinatesof thenew figureA’B’C’D’. Have students completeproblems 2 and3 independently. Skill Builders 32-5 32-6 (affect of dilation on perimeter and area) 49-1 (coordinate graphing) 52 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Dilations Similar figures, larger or smaller than the original image, can be created by multiplying the coordinates of each point by a scale factor, r . TriangleOLD is to be dilated by a scale factor of r = 2. Find the coordinates of the old image and the new image, OMP. Graph the new image. y x 0 6 4 2 O L D –2 –4 –6 2 4 6 – 6 –4 –2 O ( , ) L ( , ) D ( , ) y x 0 –2 –4 –6 – 6 –4 –2 2 4 6 6 4 2 O ( , ) M ( , ) P ( , ) The side lengths of OMP are _____ times the side lengths of OLD. Find the coordinates of the new image. Graph the new image. 1. Rectangle ABCD is dilated by a scale factor of to become rectangle A'B'C'D'. 0 –1 –2 –3 –4 –5 –1 –2 –3 –4 –5 1 2 3 4 5 6 1 2 3 4 5 D C B A 0 –1 –2 –3 –4 –5 –1 –2 –3 –4 –5 1 2 3 4 5 6 1 2 3 4 5 A' ( , ) B' ( , ) C' ( , ) D' ( , ) 2. Rectangle A'B'C'D' is a dilation of rectangle ABCD. What is the scale factor ( r ) used to create rectangle A'B'C'D'? 3. Triangle PA'B' is a dilation of PAB. What is the scale factor ( r ) used to create PA'B'? A B C D 12 6 8 4 00 00 20 2 1 0 1 2 A D B C 00 20 40 03 06 O M P r = r = 8.G.3