PRE CALCULUS Pre-Calculus Geometry 4 — Questions and Answers
Question 1: What is the equation of the line passing through (1, 3) and (4, 9)?
- y = 2x + 1 (Correct answer)
- y = 3x
- y = 2x + 3
- y = x + 2
Correct answer: y = 2x + 1
Slope = (9−3)/(4−1) = 2; using point (1,3): y − 3 = 2(x−1) → y = 2x + 1.
Question 2: In an isosceles triangle, the vertex angle is 40°. What are the base angles?
- 70° each (Correct answer)
- 60° each
- 80° each
- 50° each
Correct answer: 70° each
The two base angles are equal and sum with 40° to 180°, so each is (180°−40°)/2 = 70°.
Question 3: Which transformation maps a point (x, y) to (−x, y)?
- Reflection over the y-axis (Correct answer)
- Reflection over the x-axis
- Rotation 90°
- Translation
Correct answer: Reflection over the y-axis
Negating x while keeping y the same reflects the point across the y-axis.
Question 4: A tangent from an external point touches a circle of radius 5 at a point 12 units from the center. How long is the tangent segment?
- √119 (Correct answer)
- 13
- 7
- √109
Correct answer: √119
Tangent² = distance² − radius² = 144 − 25 = 119, so tangent = √119.
Question 5: What is the area of an equilateral triangle with side length 6?
- 9√3 (Correct answer)
- 6√3
- 12√3
- 18
Correct answer: 9√3
Area = (√3/4)s² = (√3/4)(36) = 9√3.
Question 6: Which set of side lengths can form a triangle?
- 5, 8, 11 (Correct answer)
- 1, 2, 4
- 3, 5, 9
- 2, 3, 6
Correct answer: 5, 8, 11
For (5, 8, 11): 5+8=13>11, 5+11>8, and 8+11>5 — all triangle inequality conditions hold.
Question 7: A point is rotated 180° about the origin. If the original point is (3, −5), where does it land?
- (−3, 5) (Correct answer)
- (5, −3)
- (3, 5)
- (−5, 3)
Correct answer: (−3, 5)
A 180° rotation maps (x, y) to (−x, −y), so (3, −5) → (−3, 5).
PRE CALCULUS Pre-Calculus Geometry 4
What is the equation of the line passing through (1, 3) and (4, 9)?