Calculate the distance between the points (1, 1) and (4, 5).

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Question: Calculate the distance between the points (1, 1) and (4, 5).

Options:

Correct Answer: 5

Solution:

Using the distance formula: d = √[(4 - 1)² + (5 - 1)²] = √[9 + 16] = √25 = 5.

Calculate the distance between the points (1, 1) and (4, 5).

Calculate 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: Use the distance formula, which is d = √[(x2 - x1)² + (y2 - y1)²]. Here, (x1, y1) = (1, 1) and (x2, y2) = (4, 5).
Step 3: Calculate (x2 - x1). This is 4 - 1 = 3.
Step 4: Calculate (y2 - y1). This is 5 - 1 = 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, 1) and (4, 5) is 5.

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