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In a coordinate plane, if the coordinates of points A and B are (2, 3) and (2, 7

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Question: In a coordinate plane, 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 units
  2. 5 units
  3. 6 units
  4. 7 units

Correct Answer: 4 units

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 units.

In a coordinate plane, if the coordinates of points A and B are (2, 3) and (2, 7

Practice Questions

Q1
In a coordinate plane, 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 units
  2. 5 units
  3. 6 units
  4. 7 units

Questions & Step-by-Step Solutions

In a coordinate plane, 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 distance formula: Distance = √((x2 - x1)² + (y2 - y1)²).
  • Step 3: Substitute the coordinates into the formula. Here, x1 = 2, y1 = 3, x2 = 2, and y2 = 7.
  • Step 4: Calculate (x2 - x1). This is (2 - 2) = 0.
  • Step 5: Calculate (y2 - y1). This is (7 - 3) = 4.
  • Step 6: Now substitute these values back into the formula: Distance = √((0)² + (4)²).
  • Step 7: Calculate (0)² which is 0, and (4)² which is 16.
  • Step 8: Add these results together: 0 + 16 = 16.
  • Step 9: Take the square root of 16: √16 = 4.
  • Step 10: Therefore, the distance between points A and B is 4 units.
  • Distance Formula – The distance between two points in a coordinate plane is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
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