If the coordinates of points A and B are (2, 3) and (5, 7) respectively, what is

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Question: If the coordinates of points A and B are (2, 3) and (5, 7) respectively, what is the distance AB?

Options:

Correct Answer: 5

Solution:

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

If the coordinates of points A and B are (2, 3) and (5, 7) respectively, what is the distance AB?

If the coordinates of points A and B are (2, 3) and (5, 7) respectively, what is the distance AB?

Step 1: Identify the coordinates of points A and B. Point A is (2, 3) and point B is (5, 7).
Step 2: Use the distance formula, which is Distance = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) are the coordinates of point A and (x2, y2) are the coordinates of point B.
Step 3: Substitute the coordinates into the formula. So, x1 = 2, y1 = 3, x2 = 5, and y2 = 7.
Step 4: Calculate (x2 - x1) which is (5 - 2) = 3.
Step 5: Calculate (y2 - y1) which is (7 - 3) = 4.
Step 6: Now, square the results from Step 4 and Step 5. So, (3)² = 9 and (4)² = 16.
Step 7: Add the squared results together: 9 + 16 = 25.
Step 8: Take the square root of the sum from Step 7: √25 = 5.
Step 9: The distance AB is 5.

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