PRE CALCULUS Pre-Calculus Geometry 5 — Questions and Answers
Question 1: What is the area of a triangle with vertices at (0, 0), (6, 0), and (2, 4)?
- 12 (Correct answer)
- 24
- 10
- 8
Correct answer: 12
Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)| = ½|0+24+0| = 12.
Question 2: An angle of −π/3 radians is coterminal with which positive angle?
- 5π/3 (Correct answer)
- π/3
- 4π/3
- 2π/3
Correct answer: 5π/3
Adding 2π: −π/3 + 2π = −π/3 + 6π/3 = 5π/3.
Question 3: Two secants are drawn from an external point. The external segment of one is 4 and its whole length is 12; the external segment of the other is 3. What is the whole length of the second secant?
- 16 (Correct answer)
- 12
- 9
- 18
Correct answer: 16
By the secant-secant theorem: 4 × 12 = 3 × x → x = 16.
Question 4: The diagonals of a rhombus have lengths 10 and 24. What is the side length of the rhombus?
- 13 (Correct answer)
- 17
- √61
- √119
Correct answer: 13
Each side = √((10/2)² + (24/2)²) = √(25+144) = √169 = 13.
Question 5: Which pair of angles are always supplementary in a cyclic quadrilateral?
- Opposite angles (Correct answer)
- Adjacent angles
- Consecutive angles
- Vertical angles
Correct answer: Opposite angles
In a cyclic quadrilateral, opposite angles sum to 180°, making them supplementary.
Question 6: If a polygon has interior angles summing to 1440°, how many sides does it have?
- 10 (Correct answer)
- 9
- 8
- 12
Correct answer: 10
Sum of interior angles = (n−2)×180°; solving 1440 = (n−2)×180 gives n = 10.
Question 7: A 45-45-90 triangle has a hypotenuse of 8. What is the length of each leg?
- 4√2 (Correct answer)
- 4
- 8√2
- 8/√3
Correct answer: 4√2
Each leg = hypotenuse / √2 = 8/√2 = 4√2.
PRE CALCULUS Pre-Calculus Geometry 5
What is the area of a triangle with vertices at (0, 0), (6, 0), and (2, 4)?