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In a coordinate plane, what is the distance between the points (3, 4) and (7, 1)

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Question: In a coordinate plane, what is the distance between the points (3, 4) and (7, 1)?

Options:

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

Correct Answer: 5 units

Solution: 

The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Thus, distance = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5 units.

In a coordinate plane, what is the distance between the points (3, 4) and (7, 1)

Practice Questions

Q1
In a coordinate plane, what is the distance between the points (3, 4) and (7, 1)?
  1. 5 units
  2. 4 units
  3. 3 units
  4. 6 units

Questions & Step-by-Step Solutions

In a coordinate plane, what is the distance between the points (3, 4) and (7, 1)?
  • Step 1: Identify the coordinates of the two points. The first point is (3, 4) and the second point is (7, 1).
  • Step 2: Label the coordinates. Let (x1, y1) = (3, 4) and (x2, y2) = (7, 1).
  • Step 3: Use the distance formula: Distance = √((x2 - x1)² + (y2 - y1)²).
  • Step 4: Substitute the values into the formula: Distance = √((7 - 3)² + (1 - 4)²).
  • Step 5: Calculate (7 - 3) which equals 4, and (1 - 4) which equals -3.
  • Step 6: Square the results: (4)² = 16 and (-3)² = 9.
  • Step 7: Add the squared results: 16 + 9 = 25.
  • Step 8: Take the square root of the sum: √25 = 5.
  • Step 9: Conclude that the distance between the points (3, 4) and (7, 1) is 5 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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