If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is

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Question: If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the distance AB?

Options:

Correct Answer: 2√2

Solution:

Distance AB = √((3-1)² + (4-2)²) = √(4) = 2.

If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the distance AB?

If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the distance AB?

Correct Answer: 2

Step 1: Identify the coordinates of points A and B. Point A is (1, 2) and point B is (3, 4).
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 = 1, y1 = 2, x2 = 3, and y2 = 4.
Step 4: Calculate (x2 - x1). This is (3 - 1) = 2.
Step 5: Calculate (y2 - y1). This is (4 - 2) = 2.
Step 6: Now square both results. (2)² = 4 and (2)² = 4.
Step 7: Add the squared results together. 4 + 4 = 8.
Step 8: Take the square root of the sum. √(8) = 2√2, which is approximately 2.83.

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