What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4

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Question: What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)

Options:

Correct Answer: 5

Solution:

Diagonal length = √[(5-1)² + (4-1)²] = √[16 + 9] = √25 = 5.

What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)

What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)

Step 1: Identify the coordinates of two opposite corners of the rectangle. We can use (1, 1) and (5, 4).
Step 2: Use the distance formula to find the length of the diagonal. The formula is: Diagonal length = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Substitute the coordinates into the formula. Here, (x1, y1) = (1, 1) and (x2, y2) = (5, 4).
Step 4: Calculate the differences: x2 - x1 = 5 - 1 = 4 and y2 - y1 = 4 - 1 = 3.
Step 5: Square the differences: (4)² = 16 and (3)² = 9.
Step 6: Add the squared differences: 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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