What is the distance between the points (1, 2) and (4, 6) in the coordinate plan

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Question: What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?

Options:

Correct Answer: 5

Solution:

Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?

What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?

Step 1: Identify the coordinates of the two points. The first point is (1, 2) and the second point is (4, 6).
Step 2: Label the coordinates. Let (x1, y1) = (1, 2) and (x2, y2) = (4, 6).
Step 3: Write down the distance formula: d = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the values into the formula. Replace x1 with 1, y1 with 2, x2 with 4, and y2 with 6.
Step 5: Calculate (x2 - x1): 4 - 1 = 3.
Step 6: Calculate (y2 - y1): 6 - 2 = 4.
Step 7: Square the results from Step 5 and Step 6: (3)² = 9 and (4)² = 16.
Step 8: Add the squared results together: 9 + 16 = 25.
Step 9: Take the square root of the sum: √25 = 5.
Step 10: The distance between the points (1, 2) and (4, 6) is 5.

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