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

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

Options:

Correct Answer: 5

Solution:

Distance = √((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 the coordinate plane?

What is the distance between the points (2, 3) and (5, 7) in the 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: Use the distance formula, which is Distance = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) is (2, 3) and (x2, y2) is (5, 7).
Step 3: Calculate (x2 - x1). This is (5 - 2) = 3.
Step 4: Calculate (y2 - y1). This is (7 - 3) = 4.
Step 5: Substitute these values into the formula: Distance = √((3)² + (4)²).
Step 6: Calculate (3)², which is 9.
Step 7: Calculate (4)², which is 16.
Step 8: Add the results: 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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