AST Geometry and Trigonometry 2 — Questions and Answers
Question 1: What is the slope of a line passing through the points (2, 3) and (6, 11)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (y₂−y₁)/(x₂−x₁) = (11−3)/(6−2) = 8/4 = 2.
Question 2: What is the distance between the points (1, 1) and (4, 5)?
- 3
- 5 (Correct answer)
- 7
- 4
Correct answer: 5
Distance = √((4−1)² + (5−1)²) = √(9 + 16) = √25 = 5.
Question 3: What is the midpoint of the segment connecting (0, 4) and (6, 2)?
- (3, 3) (Correct answer)
- (6, 6)
- (2, 3)
- (3, 1)
Correct answer: (3, 3)
Midpoint = ((0+6)/2, (4+2)/2) = (3, 3).
Question 4: What is the slope of a line perpendicular to y = 2x + 5?
- 2
- −2
- ½
- −½ (Correct answer)
Correct answer: −½
Perpendicular slopes are negative reciprocals; the negative reciprocal of 2 is −½.
Question 5: The equation x² + y² = 25 represents a circle with what radius?
- 5 (Correct answer)
- 25
- 10
- √5
Correct answer: 5
The standard circle equation is x² + y² = r², so r = √25 = 5.
Question 6: A line has the equation y = −3x + 7. What is the y-intercept?
- −3
- 3
- 7 (Correct answer)
- −7
Correct answer: 7
In slope-intercept form y = mx + b, the y-intercept is b = 7.
Question 7: What is the x-intercept of the line 2x + 3y = 12?
- (4, 0)
- (6, 0) (Correct answer)
- (0, 4)
- (3, 0)
Correct answer: (6, 0)
Setting y = 0: 2x = 12, so x = 6, giving the point (6, 0).
AST Geometry and Trigonometry 2
What is the slope of a line passing through the points (2, 3) and (6, 11)?