What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 6

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Question: What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 6), (8, 0), and (8, 6)?

Options:

Correct Answer: 10

Solution:

The length of the diagonal can be found using the distance formula: d = √((8 - 0)² + (6 - 0)²) = √(64 + 36) = √100 = 10.

What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 6), (8, 0), and (8, 6)?

What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 6), (8, 0), and (8, 6)?

Step 1: Identify the coordinates of two opposite corners of the rectangle. Here, we can use (0, 0) and (8, 6).
Step 2: Write down the distance formula, which is d = √((x2 - x1)² + (y2 - y1)²).
Step 3: Substitute the coordinates into the formula. Here, (x1, y1) = (0, 0) and (x2, y2) = (8, 6).
Step 4: Calculate the differences: x2 - x1 = 8 - 0 = 8 and y2 - y1 = 6 - 0 = 6.
Step 5: Square the differences: (8)² = 64 and (6)² = 36.
Step 6: Add the squared differences: 64 + 36 = 100.
Step 7: Take the square root of the sum: √100 = 10.
Step 8: Conclude that the length of the diagonal of the rectangle is 10.

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