Question

The distance between the points (x, y) and (-x, -y) will be:

• A. \( 2(x^2 + y^2) \)
• B. \( 4(x^2 + y^2) \)
• C. \( 2 \sqrt{x^2 + y^2} \)
• D. \( 4 \sqrt{x^2 + y^2} \)

Hint:

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Answer 1

The Correct Option is C

To find the distance between the points \( P(x, y) \) and \( Q(-x, -y) \), we use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, \( (x_1, y_1) = (x, y) \) and \( (x_2, y_2) = (-x, -y) \). Substituting these values into the distance formula: \[ d = \sqrt{((-x) - x)^2 + ((-y) - y)^2} \] \[ d = \sqrt{(-2x)^2 + (-2y)^2} = \sqrt{4x^2 + 4y^2} = 2 \sqrt{x^2 + y^2} \]
Step 2: Conclusion.
The distance between the points \( P(x, y) \) and \( Q(-x, -y) \) is \( 2 \sqrt{x^2 + y^2} \). So, the correct answer is (C).