What is the distance between the points (-1, -1) and (3, 3)?

What is the distance between the points (-1, -1) and (3, 3)?

Step 1: Identify the coordinates of the two points. The first point is (-1, -1) and the second point is (3, 3).
Step 2: Use the distance formula, which is d = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) = (-1, -1) and (x2, y2) = (3, 3).
Step 3: Substitute the values into the formula: d = √((3 - (-1))² + (3 - (-1))²).
Step 4: Simplify the expressions inside the parentheses: d = √((3 + 1)² + (3 + 1)²).
Step 5: Calculate the values: d = √(4² + 4²).
Step 6: Calculate the squares: d = √(16 + 16).
Step 7: Add the results: d = √32.
Step 8: Simplify √32: d = √(16 * 2) = √16 * √2 = 4√2.
Step 9: If needed, approximate the value: 4√2 ≈ 5.66.

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