PRE CALCULUS Pre-Calculus Geometry 2 — Questions and Answers
Question 1: What is the distance between the points (3, -4) and (-1, 2)?
- √52 (Correct answer)
- √40
- √32
- √60
Correct answer: √52
Distance = √((−1−3)² + (2−(−4))²) = √(16+36) = √52.
Question 2: Which equation represents a circle centered at (2, -3) with radius 5?
- (x−2)² + (y+3)² = 25 (Correct answer)
- (x+2)² + (y−3)² = 25
- (x−2)² + (y+3)² = 5
- (x+2)² + (y+3)² = 25
Correct answer: (x−2)² + (y+3)² = 25
The standard form is (x−h)² + (y−k)² = r², giving (x−2)² + (y+3)² = 25.
Question 3: A central angle of 120° in a circle of radius 6 subtends an arc of what length?
- 4π (Correct answer)
- 6π
- 8π
- 12π
Correct answer: 4π
Arc length = rθ = 6 × (2π/3) = 4π.
Question 4: What is the area of the sector with central angle 90° in a circle of radius 8?
- 16π (Correct answer)
- 32π
- 8π
- 64π
Correct answer: 16π
Area of sector = (θ/360°)πr² = (90/360)π(64) = 16π.
Question 5: The angle in standard position whose terminal side passes through (0, -5) measures:
- 270° (Correct answer)
- 180°
- 90°
- 0°
Correct answer: 270°
The point (0, -5) lies on the negative y-axis, which corresponds to 270° in standard position.
Question 6: Two parallel lines are cut by a transversal. If one co-interior (same-side interior) angle is 65°, what is the other?
- 115° (Correct answer)
- 65°
- 25°
- 130°
Correct answer: 115°
Co-interior angles are supplementary, so 180° − 65° = 115°.
Question 7: A right triangle has legs of length 7 and 24. What is the length of its hypotenuse?
- 25 (Correct answer)
- 26
- √527
- 31
Correct answer: 25
By the Pythagorean theorem: √(49 + 576) = √625 = 25.
PRE CALCULUS Pre-Calculus Geometry 2
What is the distance between the points (3, -4) and (-1, 2)?