What is the distance between the points (5, 5) and (1, 1)?

What is the distance between the points (5, 5) and (1, 1)?

Step 1: Identify the coordinates of the two points. The first point is (5, 5) and the second point is (1, 1).
Step 2: Use the distance formula, which is d = √[(x2 - x1)² + (y2 - y1)²]. Here, (x1, y1) = (5, 5) and (x2, y2) = (1, 1).
Step 3: Substitute the coordinates into the formula: d = √[(1 - 5)² + (1 - 5)²].
Step 4: Calculate (1 - 5) which equals -4. So, we have d = √[(-4)² + (-4)²].
Step 5: Calculate (-4)² which equals 16. Now, we have d = √[16 + 16].
Step 6: Add the two 16s together: 16 + 16 = 32. So, now we have d = √32.
Step 7: Simplify √32. This can be written as √(16 * 2) = √16 * √2 = 4√2.

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