What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3

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Question: What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3), (4, 0), and (4, 3)? (2022)

Options:

Correct Answer: 5

Exam Year: 2022

Solution:

Diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.

What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3), (4, 0), and (4, 3)? (2022)

What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3), (4, 0), and (4, 3)? (2022)

Step 1: Identify the coordinates of two opposite corners of the rectangle. Here, we can use (0, 0) and (4, 3).
Step 2: Use the distance formula to find the length of the diagonal. The formula is: Diagonal = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Substitute the coordinates into the formula. Here, x1 = 0, y1 = 0, x2 = 4, and y2 = 3.
Step 4: Calculate (x2 - x1)², which is (4 - 0)² = 4² = 16.
Step 5: Calculate (y2 - y1)², which is (3 - 0)² = 3² = 9.
Step 6: Add the two results together: 16 + 9 = 25.
Step 7: Take the square root of the sum: √25 = 5.
Step 8: The length of the diagonal of the rectangle is 5.

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