What is the distance between the points (0, 0) and (x, y) if the distance is 10?

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Question: What is the distance between the points (0, 0) and (x, y) if the distance is 10?

Options:

Correct Answer: x² + y² = 100

Solution:

Using the distance formula: d = √(x² + y²) = 10 implies x² + y² = 100.

What is the distance between the points (0, 0) and (x, y) if the distance is 10?

What is the distance between the points (0, 0) and (x, y) if the distance is 10?

Step 1: Understand that we want to find the distance between the point (0, 0) and another point (x, y).
Step 2: Recall the distance formula, which is d = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) is (0, 0) and (x2, y2) is (x, y).
Step 3: Substitute the points into the distance formula: d = √((x - 0)² + (y - 0)²) = √(x² + y²).
Step 4: We know the distance d is given as 10, so we set up the equation: √(x² + y²) = 10.
Step 5: To eliminate the square root, square both sides of the equation: (√(x² + y²))² = 10².
Step 6: This simplifies to x² + y² = 100.

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