Unit Quiz
Overview
Test your mastery of geometry concepts including transformations, the Pythagorean theorem, distance formula, and real-world applications. This quiz covers all unit objectives.
Quiz Questions
Question 1: A right triangle has legs of 9 and 12. Find the hypotenuse.
Show Answer
Answer: 15
c^2 = 9^2 + 12^2 = 81 + 144 = 225. c = 15.
Question 2: Point P(5, -2) is reflected over the y-axis. What are the new coordinates?
Show Answer
Answer: (-5, -2)
Reflection over y-axis negates the x-coordinate: (5, -2) becomes (-5, -2).
Question 3: Is a triangle with sides 8, 15, and 17 a right triangle? Show your work.
Show Answer
Answer: Yes
Check: 8^2 + 15^2 = 64 + 225 = 289 = 17^2. The Pythagorean theorem is satisfied.
Question 4: A figure is translated 4 units left and 5 units up. Express this as coordinate notation.
Show Answer
Answer: (x, y) → (x - 4, y + 5)
Left subtracts from x; up adds to y.
Question 5: Find the distance between points (2, 1) and (10, 7).
Show Answer
Answer: 10 units
d = sqrt[(10-2)^2 + (7-1)^2] = sqrt[64 + 36] = sqrt[100] = 10.
Question 6: A 25-foot wire is attached to the top of a 24-foot pole. How far from the base of the pole is the wire anchored?
Show Answer
Answer: 7 feet
b^2 + 24^2 = 25^2. b^2 + 576 = 625. b^2 = 49. b = 7 feet.
Question 7: Triangle ABC is rotated 180 degrees about the origin. If A(3, 4), what is A'?
Show Answer
Answer: (-3, -4)
180-degree rotation: (x, y) becomes (-x, -y). So (3, 4) becomes (-3, -4).
Question 8: A shape with vertices at (1, 1), (3, 1), (3, 4) is dilated by scale factor 2 from the origin. List the new vertices.
Show Answer
Answer: (2, 2), (6, 2), (6, 8)
Multiply each coordinate by 2: (1x2, 1x2), (3x2, 1x2), (3x2, 4x2).
Question 9: A hypotenuse is 20 cm and one leg is 16 cm. Find the other leg.
Show Answer
Answer: 12 cm
a^2 + 16^2 = 20^2. a^2 + 256 = 400. a^2 = 144. a = 12 cm.
Question 10: Which transformations preserve congruence: translation, reflection, rotation, dilation?
Show Answer
Answer: Translation, reflection, and rotation (not dilation)
These three are rigid transformations that preserve distance and shape. Dilation changes size, creating similar but not congruent figures.