Find the distance between the points (3, 4) and (7, 1).

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Question: Find the distance between the points (3, 4) and (7, 1).

Options:

Correct Answer: 5

Solution:

Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 3.6, closest option is 4.

Find the distance between the points (3, 4) and (7, 1).

Find the distance between the points (3, 4) and (7, 1).

Correct Answer: 4

Step 1: Identify the coordinates of the two points. The first point is (3, 4) and the second point is (7, 1).
Step 2: Use the distance formula, which is Distance = √[(x2 - x1)² + (y2 - y1)²]. Here, (x1, y1) = (3, 4) and (x2, y2) = (7, 1).
Step 3: Calculate (x2 - x1). This is 7 - 3 = 4.
Step 4: Calculate (y2 - y1). This is 1 - 4 = -3.
Step 5: Square the results from Step 3 and Step 4. So, (4)² = 16 and (-3)² = 9.
Step 6: Add the squared results together. This is 16 + 9 = 25.
Step 7: Take the square root of the sum from Step 6. √25 = 5.
Step 8: The distance between the points (3, 4) and (7, 1) is 5.

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