PRE CALCULUS Pre-Calculus Geometry 4

Question 1

What is the equation of the line passing through (1, 3) and (4, 9)?

Accepted Answer

y = 2x + 1

Answer

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?

Accepted Answer

70° each

Answer

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)?

Accepted Answer

Reflection over the y-axis

Answer

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?

Accepted Answer

√119

Answer

Tangent² = distance² − radius² = 144 − 25 = 119, so tangent = √119.

Question 5

What is the area of an equilateral triangle with side length 6?

Accepted Answer

9√3

Answer

Area = (√3/4)s² = (√3/4)(36) = 9√3.

PRE CALCULUS Practice Test