Guided Practice
Overview
This lesson provides structured practice with transformations and the Pythagorean theorem. Work through each problem carefully, applying the skills from previous lessons.
Practice Problems
Question 1: A triangle with vertices at (1, 2), (4, 2), and (1, 5) is translated 3 units right and 2 units down. What are the new coordinates?
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Answer: (4, 0), (7, 0), and (4, 3)
Add 3 to each x-coordinate and subtract 2 from each y-coordinate: (1+3, 2-2), (4+3, 2-2), (1+3, 5-2).
Question 2: A right triangle has legs of 6 cm and 8 cm. Find the hypotenuse.
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Answer: 10 cm
Using Pythagorean theorem: c^2 = 6^2 + 8^2 = 36 + 64 = 100. c = 10 cm.
Question 3: Point A(3, 4) is reflected over the x-axis. What are the new coordinates?
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Answer: (3, -4)
Reflection over x-axis: keep x the same, negate y. (3, 4) becomes (3, -4).
Question 4: A ladder leans against a wall. The base is 5 feet from the wall and the ladder is 13 feet long. How high up the wall does it reach?
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Answer: 12 feet
h^2 + 5^2 = 13^2. h^2 + 25 = 169. h^2 = 144. h = 12 feet.
Question 5: Triangle ABC is rotated 90 degrees clockwise about the origin. If A was at (2, 3), where is A' now?
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Answer: (3, -2)
90 degrees clockwise rotation: (x, y) becomes (y, -x). So (2, 3) becomes (3, -2).
Question 6: Is a triangle with sides 7, 24, and 25 a right triangle?
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Answer: Yes, it is a right triangle
Check: 7^2 + 24^2 = 49 + 576 = 625 = 25^2. The Pythagorean theorem holds.
Question 7: A shape is dilated with scale factor 2 from the origin. Point P(4, 3) becomes what point?
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Answer: (8, 6)
Dilation multiplies both coordinates by the scale factor: (4 x 2, 3 x 2) = (8, 6).
Question 8: Find the distance between points (1, 2) and (4, 6).
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Answer: 5 units
d = sqrt[(4-1)^2 + (6-2)^2] = sqrt[9 + 16] = sqrt[25] = 5 units.
Question 9: A rectangle is reflected over the y-axis. Which properties remain unchanged?
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Answer: Shape, size, and angles remain the same (congruent figure)
Reflections are rigid transformations - they preserve length, angle measure, and shape. Only position and orientation change.
Question 10: A right triangle has hypotenuse 15 and one leg 9. Find the other leg.
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Answer: 12
a^2 + 9^2 = 15^2. a^2 + 81 = 225. a^2 = 144. a = 12.