Find the distance between the points A(2, 3) and B(5, 7).

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Question: Find the distance between the points A(2, 3) and B(5, 7).

Options:

Correct Answer: 5

Solution:

Distance = √[(5-2)² + (7-3)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

Find the distance between the points A(2, 3) and B(5, 7).

Find the distance between the points A(2, 3) and B(5, 7).

Correct Answer: 5

Step 1: Identify the coordinates of point A, which are (2, 3).
Step 2: Identify the coordinates of point B, which are (5, 7).
Step 3: Use the distance formula: Distance = √[(x2 - x1)² + (y2 - y1)²].
Step 4: Substitute the coordinates into the formula: Distance = √[(5 - 2)² + (7 - 3)²].
Step 5: Calculate (5 - 2) which equals 3, and (7 - 3) which equals 4.
Step 6: Square the results: 3² = 9 and 4² = 16.
Step 7: Add the squared results together: 9 + 16 = 25.
Step 8: Take the square root of 25: √25 = 5.
Step 9: The distance between points A and B is 5.

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