Name Date Class. MM', and NN' on the graph for Problem 2, where would the lines intersect? (, ) This point is called the

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1 Practice and Problem Solving: A/B For Problems 1 and 2, apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points, and plot the pre-image and the image. Tell the scale factor. 1. D(x, y) (1.5x, 1.5y) G(1, 2), H(1, 4), J(4, 2) G'(, ), H'(, ), J'(, ) _ 2. D(x, y) x, y 3 3 L( 3, 3), M(3, 6), N(3, 3) L'(, ), M'(, ), N'(, ) _ For Problems 3 6, use your graphs for Problems 1 and If you drew lines G G', H H', and JJ', on the graph for Problem 1, where would the lines intersect? (, ) This point is called the of. 4. If you drew lines LL', MM', and NN' on the graph for Problem 2, where would the lines intersect? (, ) 5. Fill in the lengths of the segments in Problem 1. Express each ratio as a decimal. G'H' GH = = J'G' JG = = 6. Fill in the lengths of the segments in Problem 2. Express each ratio in radical form, if necessary, and then as a fraction in lowest terms. L'M' LM = M'N' MN = = N'L' NL = = 211

2 Reading Strategies: Use a Concept Map Use the concept map below to help you understand dilations. Definition A dilation is a transformation that can change the size of a figure but leaves the shape unchanged. Properties Preserves angle measure Preserves betweenness Preserves collinearity Preserves orientation Ratios of lengths of corresponding sides are equal. Example Dilation Nonexample Determine whether each transformation is a dilation. If it is not a dilation, explain why not. Look at the concept map for help. 1. A( 3, 5), B( 1, 5), C( 1, 1), D( 5, 1); 2. J(0, 1), K(2, 5), L(4, 1); E( 2, 4), F(2, 4), G(4, 2), H( 2, 2) M(1, 2), N(2, 1), P(3, 2) 3. D( 6, 3), E(0, 6), F(6, 3), G(5, 2), H( 5, 2); 4. P( 5, 4), Q( 1, 4), R( 1, 2), S(5, 2); J( 4, 2), K(0, 3), L(4, 2), M(2, 2), N( 2, 2) T(1, 5), U(6, 5), V(6, 1), W(1, 1) 214

3 Practice and Problem Solving: Modified For each problem, a dilation D is named. It maps each point (x, y) of the preimage to a corresponding point on the image. Name the point on the image that corresponds to each point of the given preimage. Then plot both figures and tell the scale factor. The first one is done for you. 1. Dxy (, ) x, y 2 2 Preimage: A(4, 10), B( 6, 4), C(4, 4) Image: A'(, 2 ), 5 B'(, ), C'(, ) 2. D(x, y) (3x, 3y) Preimage: P(1, 1), Q(2, 1), R( 2, 1) Image: P'(, ), Q'(, ), R'(, ) 3. D(x, y) (2x, 2y) Preimage: X(3, 1), Y( 2, 3), Z(2, 1) Image: X'(, ), Y'(, ), Z'(, ) For Problems 4 6, refer to the dilations in Problems 1 3. The first one is done for you. 4. For Problem 3, each coordinate in the preimage XYZ is multiplied by 2 to get the corresponding coordinate in the image. Each side of the image is times as long as the corresponding side of the pre-image. The scale factor for Problem 3 is. 5. Each side of the images in Problems 1 3 is to the corresponding side of its preimage. 6. In Problem 2, point P' is times as far from the origin as point P is. Point Q' is times as far from the origin as point Q is. 213

4 Practice and Problem Solving: C For Problems 1 3, apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points, and plot the preimage and the image. 1. D(x, y) (0.75x, 0.75y) E( 4, 6), F( 2, 2), G(4, 2), H(4, 4) E'(, ), F'(, ), G'(, ), H'(, ) 2. D(x, y) (2(x + 2), 2(y 3)) J( 2, 2), K( 4, 1), L(1, 0) J'(, ), K'(, ), L'(, ) 3. D(x, y) ( x 1, ) ( y + 2) 3 3 X( 5, 5), Y( 2, 4), Z(4, 4) X'(, ), Y'(, ), Z'(, ) To solve Problems 4 7, refer to your graphs for Problems In Problem 1, find the lengths of H'G' and HG. H'G' =. HG =. Write the ratio H'G' HG as a fraction in lowest terms. What is the scale factor? 5. In Problem 2, find J'L' and JL in radical form. Write their ratio and simplify. In Problem 3, find the ratio of X'Y' and XY and simplify. 6. In Problem 1, if you drew E E', FF', G G', and H H', where would they intersect? This is the center of dilation. 7. Find the center of dilation for Problem

5 Reteach A dilation is a transformation of a figure that changes the size but not the shape of the figure. DEF is a dilation of ABC. DEF is the same shape as ABC. The corresponding angles of ABC and DEF are congruent. A D, B E, and C F The ratios of the corresponding side lengths are equal. Each side of DEF has a length that is twice the length of the corresponding side in ABC. So, the scale factor of the dilation is 2. WXYZ is a dilation of PQRS. 1. m P = 80, m W 2. WZ = 3. WX = = 4. What is the scale factor? Is DEF a dilation of ABC? Explain your answer