In this quiz, we test our understanding of how to find the distance between two points on the coordinate plane.
Try to answer the questions before checking the answers at the bottom of the page.
Instructions
For two points:
$$P_1=(x_1,y_1)$$
and
$$P_2=(x_2,y_2)$$
use:
$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$
Remember:
- Find the difference between the \(x\)-coordinates.
- Find the difference between the \(y\)-coordinates.
- Square both differences.
- Add them.
- Take the square root.
Question 1
Find the distance between:
$$P_1=(1,2)$$
and
$$P_2=(4,6)$$
A) \(3\)
B) \(4\)
C) \(5\)
D) \(7\)
Question 2
Find the distance between:
$$P_1=(0,0)$$
and
$$P_2=(3,4)$$
A) \(4\)
B) \(5\)
C) \(6\)
D) \(7\)
Question 3
Find the distance between:
$$P_1=(-1,2)$$
and
$$P_2=(2,6)$$
A) \(3\)
B) \(4\)
C) \(5\)
D) \(6\)
Question 4
Find the distance between:
$$P_1=(2,-3)$$
and
$$P_2=(8,-3)$$
A) \(5\)
B) \(6\)
C) \(8\)
D) \(11\)
Question 5
Find the distance between:
$$P_1=(-4,1)$$
and
$$P_2=(-4,8)$$
A) \(4\)
B) \(6\)
C) \(7\)
D) \(8\)
Question 6
Find the distance between:
$$P_1=(-2,-1)$$
and
$$P_2=(1,3)$$
A) \(4\)
B) \(5\)
C) \(6\)
D) \(7\)
Question 7
Find the distance between:
$$P_1=(0,0)$$
and
$$P_2=(2,3)$$
A) \(\sqrt{5}\)
B) \(\sqrt{10}\)
C) \(\sqrt{13}\)
D) \(\sqrt{17}\)
Question 8
If two points have the same \(y\)-coordinate, the distance between them is:
A) horizontal
B) vertical
C) always zero
D) always diagonal
Question 9
If two points have the same \(x\)-coordinate, the distance between them is:
A) horizontal
B) vertical
C) always zero
D) always diagonal
Question 10
Why does the distance formula work in \(2D\)?
A) It comes from the area formula.
B) It comes from the Pythagorean Theorem.
C) It comes from the circumference formula.
D) It comes from the exterior angle theorem.
Answers
- C) \(5\)
- B) \(5\)
- C) \(5\)
- B) \(6\)
- C) \(7\)
- B) \(5\)
- C) \(\sqrt{13}\)
- A) horizontal
- B) vertical
- B) It comes from the Pythagorean Theorem.
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