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(Bluebonnet: p. 158) A triangle has a base of 10 units and a height of 8 units. Both dimensions are...

Question 3 (Bluebonnet: p. 158)
A triangle has a base of 10 units and a height of 8 units. Both dimensions are multiplied by 3. What is the new area, and how does it compare with the original area?
A. 120 square units; 3 times the original area
B. 240 square units; 6 times the original area
C. 360 square units; 9 times the original area
D. 1,080 square units; 27 times the original area
Question 4 (Bluebonnet: p. 215)
Trapezoid A′B′C′D′ is the image of trapezoid ABCD under (x, y) → (x + 6, y − 3). The image vertices are A′(8, −1), B′(14, −1), C′(12, 2), and D′(9, 2). Determine the original vertices.
A. A(14, −4), B(20, −4), C(18, −1), D(15, −1)
B. A(2, −4), B(8, −4), C(6, −1), D(3, −1)
C. A(14, 2), B(20, 2), C(18, 5), D(15, 5)
D. A(2, 2), B(8, 2), C(6, 5), D(3, 5)

Answer

Question 3: C. 360 square units; 9 times the original area. The original area is (1/2)(10)(8) = 40 square units. The new base and height are 30 and 24 units, so the new area is (1/2)(30)(24) = 360 square units, which is 360/40 = 9 times the original.

Question 4: D. A(2, 2), B(8, 2), C(6, 5), D(3, 5). Reverse the translation by subtracting 6 from each image x-coordinate and adding 3 to each image y-coordinate: (x′, y′) → (x′ − 6, y′ + 3).

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