PRE CALCULUS Pre-Calculus Geometry 3

Question 1

What is the midpoint of the segment joining (−4, 6) and (8, −2)?

Accepted Answer

(2, 2)

Answer

Midpoint = ((−4+8)/2, (6+(−2))/2) = (2, 2).

Question 2

Which of the following is a Pythagorean triple?

Accepted Answer

8, 15, 17

Answer

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?

Accepted Answer

4

Answer

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:

Accepted Answer

5√3

Answer

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?

Accepted Answer

−4/3

Answer

Perpendicular slopes are negative reciprocals, so the slope is −4/3.

PRE CALCULUS Practice Test