What is the distance between the points (2, 3) and (6, 7)?

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Question: What is the distance between the points (2, 3) and (6, 7)?

Options:

Correct Answer: 5

Solution:

Using the distance formula: d = √[(6 - 2)² + (7 - 3)²] = √[16 + 16] = √32 = 4√2 ≈ 5.66.

What is the distance between the points (2, 3) and (6, 7)?

What is the distance between the points (2, 3) and (6, 7)?

Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (6, 7).
Step 2: Use the distance formula, which is d = √[(x2 - x1)² + (y2 - y1)²]. Here, (x1, y1) = (2, 3) and (x2, y2) = (6, 7).
Step 3: Calculate the difference in the x-coordinates: x2 - x1 = 6 - 2 = 4.
Step 4: Calculate the difference in the y-coordinates: y2 - y1 = 7 - 3 = 4.
Step 5: Square the differences: (4)² = 16 and (4)² = 16.
Step 6: Add the squared differences: 16 + 16 = 32.
Step 7: Take the square root of the sum: √32.
Step 8: Simplify √32 to 4√2.
Step 9: If needed, approximate 4√2 to about 5.66.

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