PRE CALCULUS Pre-Calculus Geometry 5

Question 1

What is the area of a triangle with vertices at (0, 0), (6, 0), and (2, 4)?

Accepted Answer

12

Answer

Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)| = ½|0+24+0| = 12.

Question 2

An angle of −π/3 radians is coterminal with which positive angle?

Accepted Answer

5π/3

Answer

Adding 2π: −π/3 + 2π = −π/3 + 6π/3 = 5π/3.

Question 3

Two secants are drawn from an external point. The external segment of one is 4 and its whole length is 12; the external segment of the other is 3. What is the whole length of the second secant?

Accepted Answer

16

Answer

By the secant-secant theorem: 4 × 12 = 3 × x → x = 16.

Question 4

The diagonals of a rhombus have lengths 10 and 24. What is the side length of the rhombus?

Accepted Answer

13

Answer

Each side = √((10/2)² + (24/2)²) = √(25+144) = √169 = 13.

Question 5

Which pair of angles are always supplementary in a cyclic quadrilateral?

Accepted Answer

Opposite angles

Answer

In a cyclic quadrilateral, opposite angles sum to 180°, making them supplementary.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

PRE CALCULUS Pre-Calculus Geometry 5