Question

If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is

• A. a square
• B. a circle
• C. a straight line
• D. two intersecting lines

Answer 1

The Correct Option is A

Given: The sum of the distances of a point from two perpendicular lines is 1 unit. Step 1: Assume coordinate system Let the two perpendicular lines be the coordinate axes: - The x-axis: \( y = 0 \) - The y-axis: \( x = 0 \) Let the point be \( (x, y) \). Then the perpendicular distance from the x-axis is \( |y| \), and from the y-axis is \( |x| \). Step 2: Use the given condition The sum of distances is 1: \[ |x| + |y| = 1 \] Step 3: Analyze the equation The equation \( |x| + |y| = 1 \) represents a square in the coordinate plane, with its sides inclined at 45°, and vertices at: \[ (1, 0),\ (0, 1),\ (-1, 0),\ (0, -1) \] It is a square centered at the origin, aligned along the axes. Final Answer: \[ \boxed{\text{a square}} \]