In this quiz, we test our understanding of how to use the distance formula to find the radius and area of a circle.
Try to answer the questions before checking the answers at the bottom of the page.
Instructions
If the center is:
$$C=(x_1,y_1)$$
and a point on the circle is:
$$P=(x_2,y_2)$$
find the radius using:
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$
Then find the area using:
$$A=\pi r^2$$
Question 1
A circle has center:
$$C=(0,0)$$
and passes through:
$$P=(3,4)$$
What is the radius?
A) \(3\)
B) \(4\)
C) \(5\)
D) \(7\)
Question 2
If:
$$r=5$$
what is the area of the circle?
A) \(5\pi\)
B) \(10\pi\)
C) \(25\pi\)
D) \(50\pi\)
Question 3
A circle has center:
$$C=(2,1)$$
and passes through:
$$P=(6,1)$$
What is the radius?
A) \(2\)
B) \(3\)
C) \(4\)
D) \(6\)
Question 4
For the circle in Question 3, what is the area?
A) \(4\pi\)
B) \(8\pi\)
C) \(16\pi\)
D) \(36\pi\)
Question 5
A circle has center:
$$C=(-2,-1)$$
and passes through:
$$P=(-2,5)$$
What is the radius?
A) \(4\)
B) \(5\)
C) \(6\)
D) \(7\)
Question 6
A circle has center:
$$C=(-1,1)$$
and passes through:
$$P=(3,4)$$
What is the radius?
A) \(3\)
B) \(4\)
C) \(5\)
D) \(6\)
Question 7
For the circle in Question 6, what is the area?
A) \(10\pi\)
B) \(20\pi\)
C) \(25\pi\)
D) \(30\pi\)
Question 8
Why can we use the distance formula to find the radius of a circle?
A) Because the radius is the distance from the center to a point on the circle.
B) Because the radius is always equal to the area.
C) Because every circle has radius \(1\).
D) Because the radius is the distance between any two points on the circle.
Question 9
Which formula gives the area of a circle?
A) \(A=2\pi r\)
B) \(A=\pi r^2\)
C) \(A=\pi d\)
D) \(A=r^2\)
Question 10
A circle has radius:
$$r=3$$
What is its area?
A) \(3\pi\)
B) \(6\pi\)
C) \(9\pi\)
D) \(18\pi\)
Answers
- C) \(5\)
- C) \(25\pi\)
- C) \(4\)
- C) \(16\pi\)
- C) \(6\)
- C) \(5\)
- C) \(25\pi\)
- A) Because the radius is the distance from the center to a point on the circle.
- B) \(A=\pi r^2\)
- C) \(9\pi\)
Practice
- More Examples
- Take the Quiz (Current page)
Continue Learning
- Plotting Points on the Coordinate Plane (\(2D\))
- Which Quadrant or Axis? Points on the Coordinate Plane \(2D\)
- Distance Formula in \(2D\)
- Distance between Two Points in \(2D\)
- Distance Formula: Radius and Area of a Circle