In a coordinate plane, what is the distance between the points (1, 2) and (4, 6)

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Question: In a coordinate plane, what is the distance between the points (1, 2) and (4, 6)?

Options:

Correct Answer: 5 units

Solution:

Distance = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

In a coordinate plane, what is the distance between the points (1, 2) and (4, 6)?

In a coordinate plane, what is the distance between 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 Distance = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) is (1, 2) and (x2, y2) is (4, 6).
Step 3: Calculate (x2 - x1). This is (4 - 1) = 3.
Step 4: Calculate (y2 - y1). This is (6 - 2) = 4.
Step 5: Square the results from Step 3 and Step 4. So, (3)² = 9 and (4)² = 16.
Step 6: Add the squared results together. This is 9 + 16 = 25.
Step 7: Take the square root of the sum from Step 6. √25 = 5.
Step 8: The distance between the points (1, 2) and (4, 6) is 5 units.

Distance Formula – The distance between two points in a coordinate plane is calculated using the formula √((x2 - x1)² + (y2 - y1)²).