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Unit 5 review QUESTION 1 A transformation where a geometric figure is reduced or enlarged in the coordinate plane is called a _____________________ #1 - answer Dilation QUESTION 2 Figures that are exactly the same size and the same shape are ________________ figures. #2 - answer congruent QUESTION 3 List the characteristics of similar figures. #3 - answer *same shape *corresponding angles are congruent *corresponding sides are proportional QUESTION 4 One vertex of a triangle on the coordinate plane has the ordered pair of (32, 16). The rectangle undergoes a ¼ dilation. What would be the new coordinates of the corresponding vertex? #4 - answer (8, 4) Question 5 • Cheryl wants to dilate a photograph that has a width of 17.5 inches and a length of 24.5 inches to fit into a frame that is 7 inches in length. What will be the width of the new photograph? #5 - answer 5 inches You can set up a proportion. Or, you can divide 24.5 by 7, which equals 3.5. Then, divide 17.5 by 3.5. Question 6 • Stacey decides to dilate the area of her rectangular garden. The length of her original garden is 10 feet and the area is 45 square feet. The length of the new garden will be 15 feet. What is the area of the new garden? #6 - answer 101.25 ft² A = 45 ft² 4.5 ft 10 ft Scale Factor = 1.5 Area Scale Factor = 2.25 A = 101.25 ft² 15 ft 6.75 ft Question 7 Find the value of x if triangle ABC ~ triangle JPH A J x 15 H 12 C 66 B P #7 - answer • X = 82.5 Question 8 • Determine the scale factor of the first figure to the second figure. 7 in 11 in #8 - answer 11/ 7 in Question 9 State whether the dilation would be reduced, enlarged, or congruent. Scale factor = 1/17 #9 - answer reduced Question 10 State whether the dilation would be reduced, enlarged, or congruent. Scale factor = 17 #10 - answer enlarged Question 11 • A vertex of a rectangle on the coordinate plane is (-4, -2). The rectangle is dilated and the new coordinate of the vertex is (-2, -1). What was the scale factor of the dilation? #11 - answer 1/2 Question 12 State whether the dilation would be reduced, enlarged, or congruent. Scale factor = 1 #12 - answer congruent Question 13 If triangle ABC ~ triangle JPH. Which proportion can be used to find the value of x? A J x 15 H 12 C 66 B P #13 - answer Question 14 Determine the scale factor from the reduction of the first figure to the second figure. 3 5 #14 - answer 3 5 Question 15 Find the area of the smaller similar rectangle. 8 x 4 16 #15 - answer Area = 8 *scale factor is 4/16 or ¼. 8 times ¼ = 2. Therefore, x = 2. Area = length times width 8=2•4 Question 16 Find the area of the larger similar rectangle. x 5 4 14 #16 - answer Area = 245 14 ÷ 4 = 3.5 x = 5 • 3.5 x = 17.5 17.5 • 14 = 245 Question 17 If rectangle ABCD ~ rectangle WXYZ, what side corresponds with YZ? #17 - answer CD Question 18 Rectangle ABCD ~ rectangle WXYZ. Is WX congruent to BC? #18 - answer No Question 19 Are all squares similar? #19 - answer Yes Question 20 A flagpole is 28 ft tall and has a shadow of 20 ft. How tall is a nearby tree if its shadow is 30 ft? #20 - answer 42 feet Question 21 Triangle ABC ~ to triangle WXY. Use the diagram to find the perimeter of triangle ABC. A W 5m 4m X 3m B 21 m C Y #21 - answer The area of the large triangle is 84 m. *3 • 7 = 21 Therefore, the scale factor is 7. 4 • 7 = 28 and 5 • 7 = 35. Add the sides of the large triangle to get the perimeter. 28 + 35 + 21 = 84 m. Question 22 21 in x in 12 in 7 in #22 - answer x = 4 in Question 23 One vertex of a triangle on the coordinate plane has the ordered pair of (24, 16). The triangle undergoes 1/8 dilation. What would be the new coordinates of the corresponding vertex? #23 - answer (3, 2) Question 24 • Brooke is 5 ft tall. She and her class are walking through a wooded area looking for a tree that is 50 ft. tall. If the length of Brooke’s shadow is 2 ft, how will the students know when they have found a 50 ft tree? #24 - answer • When they find a tree’s shadow that measures 20 feet. Question 25 • A shrub is 1.5 meters tall and casts a shadow 3.5 meters long. At the same time, a radio tower casts a shadow 98 meters long. How tall is the radio tower? #25 - answer 42 meters Question 26 Linda wants to enlarge a 5 inch by 7 inch photograph that will fit into a frame that is 21 inches long. What is the width of the new photograph? #26 - answer • 15 inches 5 in 7 in 21 in 21/7 = 3 (scale factor) 5 • 3 = 15