What is the distance between the points (1, 1) and (4, 5)?

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Question: What is the distance between the points (1, 1) and (4, 5)?

Options:

Correct Answer: 5

Solution:

Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(4 - 1)² + (5 - 1)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

What is the distance between the points (1, 1) and (4, 5)?

What is the distance between the points (1, 1) and (4, 5)?

Step 1: Identify the coordinates of the two points. The first point is (1, 1) and the second point is (4, 5).
Step 2: Label the coordinates. Let (x1, y1) = (1, 1) and (x2, y2) = (4, 5).
Step 3: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 4: Substitute the values into the formula: d = √[(4 - 1)² + (5 - 1)²].
Step 5: Calculate (4 - 1) and (5 - 1): (4 - 1) = 3 and (5 - 1) = 4.
Step 6: Substitute these results back into the formula: d = √[3² + 4²].
Step 7: Calculate 3² and 4²: 3² = 9 and 4² = 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 (1, 1) and (4, 5) is 5.

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