What is the distance between the points (2, 3) and (5, 7) in a coordinate plane?

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Question: What is the distance between the points (2, 3) and (5, 7) in a coordinate plane?

Options:

Correct Answer: 5

Solution:

Distance = √((x2 - x1)² + (y2 - y1)²) = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

What is the distance between the points (2, 3) and (5, 7) in a coordinate plane?

What is the distance between the points (2, 3) and (5, 7) in a coordinate plane?

Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (5, 7).
Step 2: Label the coordinates. Let (x1, y1) = (2, 3) and (x2, y2) = (5, 7).
Step 3: Use the distance formula: Distance = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the values into the formula: Distance = √((5 - 2)² + (7 - 3)²).
Step 5: Calculate (5 - 2) and (7 - 3): (5 - 2) = 3 and (7 - 3) = 4.
Step 6: Substitute these results back into the formula: Distance = √(3² + 4²).
Step 7: Calculate 3² and 4²: 3² = 9 and 4² = 16.
Step 8: Add the squares together: 9 + 16 = 25.
Step 9: Take the square root of 25: √25 = 5.
Step 10: The distance between the points (2, 3) and (5, 7) is 5.

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