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

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

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

Steps: 9

Step 1: Identify the coordinates of two opposite corners of the rectangle. Here, we can use (0, 0) and (3, 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) = (0, 0) and (x2, y2) = (3, 4).
Step 4: Calculate (x2 - x1) which is (3 - 0) = 3.
Step 5: Calculate (y2 - y1) which is (4 - 0) = 4.
Step 6: Square the results from Step 4 and Step 5. So, (3)² = 9 and (4)² = 16.
Step 7: Add the squared results together: 9 + 16 = 25.
Step 8: Take the square root of the sum from Step 7: √25 = 5.
Step 9: The length of the diagonal of the rectangle is 5.