PRE CALCULUS Pre-Calculus Geometry 3 — Questions and Answers
Question 1: What is the midpoint of the segment joining (−4, 6) and (8, −2)?
- (2, 2) (Correct answer)
- (4, 4)
- (2, 4)
- (−2, 2)
Correct answer: (2, 2)
Midpoint = ((−4+8)/2, (6+(−2))/2) = (2, 2).
Question 2: Which of the following is a Pythagorean triple?
- 8, 15, 17 (Correct answer)
- 6, 8, 11
- 5, 12, 14
- 9, 12, 16
Correct answer: 8, 15, 17
8² + 15² = 64 + 225 = 289 = 17², confirming (8, 15, 17) is a Pythagorean triple.
Question 3: A circle has equation x² + y² − 6x + 4y − 3 = 0. What is its radius?
- 4 (Correct answer)
- 16
- √3
- 3
Correct answer: 4
Completing the square: (x−3)² + (y+2)² = 16, so radius = 4.
Question 4: In a 30-60-90 triangle, if the hypotenuse is 10, the side opposite 60° is:
- 5√3 (Correct answer)
- 5
- 10√3
- 5√2
Correct answer: 5√3
In a 30-60-90 triangle the side opposite 60° = (√3/2) × hypotenuse = 5√3.
Question 5: What is the slope of the line perpendicular to y = (3/4)x + 2?
- −4/3 (Correct answer)
- 4/3
- 3/4
- −3/4
Correct answer: −4/3
Perpendicular slopes are negative reciprocals, so the slope is −4/3.
Question 6: Convert 5π/6 radians to degrees.
- 150° (Correct answer)
- 120°
- 135°
- 160°
Correct answer: 150°
(5π/6) × (180°/π) = 150°.
Question 7: If two chords intersect inside a circle and the segments of one chord are 3 and 8, while one segment of the other chord is 4, what is the remaining segment?
- 6 (Correct answer)
- 4
- 8
- 12
Correct answer: 6
By the intersecting chords theorem: 3 × 8 = 4 × x, so x = 6.
PRE CALCULUS Pre-Calculus Geometry 3
What is the midpoint of the segment joining (−4, 6) and (8, −2)?