Question

The sum of the distances of a point P from two perpendicular lines in plane is 1 Then locus of p is

• A. Square
• B. Circle
• C. Straight Line
• D. Pair of straight lines

Answer 1

The correct option is A Square

We have,

Let the $x$ and $y$ axes be perpendicular lines.

According to given question

Sum of the distance would be $x+y=1$

So, in the first quadrant, the locus of points would look like a straight line with points $(0,1)$ and $(1,0)$.

In the second quadrant, the locus of points would look like a straight line with points $(0,1)$ and $(-1,0)$.

In the Third quadrant, the locus of points would look like a straight line with points $(0,-1)$ and $(1,0)$.

When you put it all together, it would be a square ${45}^o$ degree about the origin.

The length of the side of the square would be $\sqrt{2}$.

Hence, this is the answer.