Calculate the distance between the points (6, 8) and (2, 3).

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Question: Calculate the distance between the points (6, 8) and (2, 3).

Options:

Correct Answer: 6

Solution:

Using the distance formula: d = √[(2 - 6)² + (3 - 8)²] = √[16 + 25] = √41.

Calculate the distance between the points (6, 8) and (2, 3).

Calculate the distance between the points (6, 8) and (2, 3).

Step 1: Identify the coordinates of the two points. The first point is (6, 8) and the second point is (2, 3).
Step 2: Use the distance formula, which is d = √[(x2 - x1)² + (y2 - y1)²]. Here, (x1, y1) = (6, 8) and (x2, y2) = (2, 3).
Step 3: Substitute the values into the formula: d = √[(2 - 6)² + (3 - 8)²].
Step 4: Calculate (2 - 6) which is -4, and then square it: (-4)² = 16.
Step 5: Calculate (3 - 8) which is -5, and then square it: (-5)² = 25.
Step 6: Add the two squared values together: 16 + 25 = 41.
Step 7: Take the square root of 41: d = √41.

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