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If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance

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Question: If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance between points A and B?

Options:

  1. 5
  2. 4
  3. 3
  4. 6

Correct Answer: 5

Solution: 

The distance between two points (x1, y1) and (x2, y2) is given by the formula: √((x2 - x1)² + (y2 - y1)²). Thus, distance = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance

Practice Questions

Q1
If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance between points A and B?
  1. 5
  2. 4
  3. 3
  4. 6

Questions & Step-by-Step Solutions

If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance between points A and B?
  • Step 1: Identify the coordinates of point A, which are (1, 2). This means x1 = 1 and y1 = 2.
  • Step 2: Identify the coordinates of point B, which are (4, 6). This means x2 = 4 and y2 = 6.
  • Step 3: Write down the distance formula: distance = √((x2 - x1)² + (y2 - y1)²).
  • Step 4: Substitute the values into the formula: distance = √((4 - 1)² + (6 - 2)²).
  • Step 5: Calculate (4 - 1) which equals 3, and (6 - 2) which equals 4.
  • Step 6: Now substitute these results back into the formula: distance = √(3² + 4²).
  • Step 7: Calculate 3² which equals 9, and 4² which equals 16.
  • Step 8: Add these two results together: 9 + 16 equals 25.
  • Step 9: Take the square root of 25, which equals 5.
  • Step 10: Therefore, the distance between points A and B is 5.
  • Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
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