If the coordinates of point A are (1, 2) and point B are (4, 6), what is the len

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Question: If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)

Options:

Correct Answer: 5

Solution:

Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)

If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)

Step 1: Identify the coordinates of point A, which are (1, 2). This means A is at x = 1 and y = 2.
Step 2: Identify the coordinates of point B, which are (4, 6). This means B is at x = 4 and y = 6.
Step 3: Use the distance formula to find the length of AB. The formula is Length AB = √[(x2 - x1)² + (y2 - y1)²].
Step 4: Substitute the coordinates into the formula. Here, x1 = 1, y1 = 2, x2 = 4, and y2 = 6.
Step 5: Calculate (x2 - x1), which is (4 - 1) = 3.
Step 6: Calculate (y2 - y1), which is (6 - 2) = 4.
Step 7: Square the results from Step 5 and Step 6. So, (3)² = 9 and (4)² = 16.
Step 8: Add the squared results together: 9 + 16 = 25.
Step 9: Take the square root of the sum from Step 8: √25 = 5.
Step 10: The length of 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].