Chapter 2 Part B

Question 1

Question: What is a circumcircle of a triangle?

Answer 1

Answer: A circumcircle is a unique circle that passes through all three vertices of a triangle. The center of the circle is the circumcentre, where the perpendicular bisectors of the triangle’s sides intersect.

Question 2

Question: What is special about the circumcircle of a right-angled triangle?

Answer 2

Answer: In a right-angled triangle, the hypotenuse is the diameter of the circumcircle. The angle in a semicircle is always a right angle.

Question 3

Question: How do you find the center of a circle given three points on the circumference?

Answer 3

Answer:

Find the equations of the perpendicular bisectors of two different chords.

Solve for the intersection of the perpendicular bisectors. This point is the center of the circle.

Question 4

What is a line segment?

Answer 4

A finite part of a straight line with two distinct endpoints.

Question 5

1. Asymptote:

Answer 5

An asymptote is a straight line that a curve approaches but never touches as the curve extends to infinity. Asymptotes can be horizontal, vertical, or oblique (slanted) and represent the behavior of the graph of a function at extreme values (e.g., as x → ∞ or x → -∞).

Example: The graph of y = 1/x has two asymptotes:

A vertical asymptote at x = 0.
A horizontal asymptote at y = 0.

Question 6

What is an inverse function?

Answer 6

An inverse function reverses the effect of the original function. If f(x) maps x to y, then the inverse function f⁻¹(x) maps y back to x.

Conditions:

The function must be one-to-one (pass the horizontal line test).
The function must be onto.
Example: If f(x) = 2x + 3, the inverse function is f⁻¹(x) = (x - 3) / 2, as it reverses the transformation applied by f(x).