If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance

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Question: If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance AB?

Options:

Correct Answer: 5

Solution:

Distance AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance AB?

If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance AB?

Step 1: Identify the coordinates of point A, which are (1, 2).
Step 2: Identify the coordinates of point B, which are (4, 6).
Step 3: Use the distance formula: Distance AB = √[(x2 - x1)² + (y2 - y1)²].
Step 4: Substitute the coordinates into the formula: Distance AB = √[(4 - 1)² + (6 - 2)²].
Step 5: Calculate (4 - 1) which equals 3, and (6 - 2) which equals 4.
Step 6: Now substitute these values: Distance AB = √[3² + 4²].
Step 7: Calculate 3² which is 9, and 4² which is 16.
Step 8: Add these two results together: 9 + 16 equals 25.
Step 9: Take the square root of 25: √25 equals 5.
Step 10: Therefore, 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].