What is the length of the line segment connecting the points (1, 2) and (4, 6)?

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Question: What is the length of the line segment connecting the points (1, 2) and (4, 6)?

Options:

Correct Answer: 5.0

Solution:

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.0.

What is the length of the line segment connecting the points (1, 2) and (4, 6)?

What is the length of the line segment connecting the points (1, 2) and (4, 6)?

Step 1: Identify the coordinates of the two points. The first point is (1, 2) and the second point is (4, 6).
Step 2: Use the distance formula, which is d = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) is (1, 2) and (x2, y2) is (4, 6).
Step 3: Substitute the values into the formula: d = √((4 - 1)² + (6 - 2)²).
Step 4: Calculate (4 - 1) which is 3, and (6 - 2) which is 4.
Step 5: Now square these results: (3)² = 9 and (4)² = 16.
Step 6: Add the squared results together: 9 + 16 = 25.
Step 7: Take the square root of 25: √25 = 5.
Step 8: The length of the line segment connecting the points (1, 2) and (4, 6) is 5.

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