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If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is

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Question: If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the distance between points A and B?

Options:

  1. 4
  2. 5
  3. 6
  4. 7

Correct Answer: 4

Solution: 

The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Here, distance = √((2 - 2)² + (7 - 3)²) = √(0 + 16) = 4.

If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is

Practice Questions

Q1
If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the distance between points A and B?
  1. 4
  2. 5
  3. 6
  4. 7

Questions & Step-by-Step Solutions

If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the distance between points A and B?
  • Step 1: Identify the coordinates of points A and B. Point A is (2, 3) and point B is (2, 7).
  • Step 2: Write down the formula for the distance between two points: distance = √((x2 - x1)² + (y2 - y1)²).
  • Step 3: Assign the coordinates to the formula. Here, x1 = 2, y1 = 3, x2 = 2, and y2 = 7.
  • Step 4: Substitute the values into the formula: distance = √((2 - 2)² + (7 - 3)²).
  • Step 5: Calculate (2 - 2) which equals 0, and (7 - 3) which equals 4.
  • Step 6: Now substitute these results back into the formula: distance = √(0² + 4²).
  • Step 7: Calculate 0² which is 0, and 4² which is 16.
  • Step 8: Now the formula looks like this: distance = √(0 + 16).
  • Step 9: Simplify it to distance = √16.
  • Step 10: Finally, calculate the square root of 16, which is 4. Therefore, the distance between points A and B is 4.
  • Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula √((x2 - x1)² + (y2 - y1)²). This question tests the application of this formula.
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