Quiz – Distance Formula in \(2D\)

In this quiz, we test our understanding of the distance formula in \(2D\) and 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 the distance formula:

$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

Remember:

  • Subtract the \(x\)-coordinates.
  • Subtract the \(y\)-coordinates.
  • Square both differences.
  • Add the results.
  • Take the square root.

Question 1

Which formula gives the distance between two points in \(2D\)?

A) \(d=(x_2-x_1)+(y_2-y_1)\)

B) \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

C) \(d=\sqrt{x_2^2+y_2^2}\)

D) \(d=|x_2-x_1|\)

Question 2

Find the distance between:

$$P_1=(1,2)$$

and

$$P_2=(4,6)$$

A) \(3\)
B) \(4\)
C) \(5\)
D) \(7\)

Question 3

Find the distance between:

$$P_1=(2,0)$$

and

$$P_2=(7,0)$$

A) \(3\)
B) \(5\)
C) \(7\)
D) \(9\)

Question 4

Find the distance between:

$$P_1=(3,1)$$

and

$$P_2=(3,6)$$

A) \(3\)
B) \(4\)
C) \(5\)
D) \(6\)

Question 5

Find the distance between:

$$P_1=(-1,-1)$$

and

$$P_2=(2,3)$$

A) \(4\)
B) \(5\)
C) \(6\)
D) \(7\)

Question 6

Find the distance between:

$$P_1=(0,0)$$

and

$$P_2=(6,8)$$

A) \(8\)
B) \(10\)
C) \(12\)
D) \(14\)

Question 7

Find the distance between:

$$P_1=(1,1)$$

and

$$P_2=(3,4)$$

A) \(\sqrt{5}\)

B) \(\sqrt{10}\)

C) \(\sqrt{13}\)

D) \(\sqrt{17}\)

Question 8

If two points have the same \(y\)-coordinate, what type of movement is there between them?

A) Horizontal only
B) Vertical only
C) Both horizontal and vertical
D) No movement

Question 9

If two points have the same \(x\)-coordinate, what type of movement is there between them?

A) Horizontal only
B) Vertical only
C) Both horizontal and vertical
D) No movement

Question 10

The distance formula in \(2D\) is based on which theorem?

A) Exterior Angle Theorem
B) Pythagorean Theorem
C) Triangle Angle Sum
D) Area of a Circle

Answers

  1. B) \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
  2. C) \(5\)
  3. B) \(5\)
  4. C) \(5\)
  5. B) \(5\)
  6. B) \(10\)
  7. C) \(\sqrt{13}\)
  8. A) Horizontal only
  9. B) Vertical only
  10. B) Pythagorean Theorem

Practice

Continue Learning

  1. Plotting Points on the Coordinate Plane (\(2D\))
  2. Which Quadrant or Axis? Points on the Coordinate Plane \(2D\)
  3. Distance Formula in \(2D\)
  4. Distance between Two Points in \(2D\)
  5. Distance Formula: Radius and Area of a Circle

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