Question

A ray of light \(x+y=1\) gets reflected upon the X-axis. If the reflected ray forms a triangle with X-axis and the vertical line \(x=2\), then the area of that triangle is

• A. \(\frac{1}{2}\)
• B. \(1\)
• C. \(2\)
• D. \(4\)

Hint:

Reflection in X-axis means replace \(y\) by \(-y\).

Answer 1

The Correct Option is A

Concept: Reflection in the X-axis changes the sign of the \(y\)-coordinate. Thus the reflected line is obtained by replacing \(y\) by \(-y\).

Step 1: Reflect the given line.
Original: \[ x+y=1 \] After reflection: \[ x-y=1 \] \[ y=x-1 \]

Step 2: Find intersections.
With X-axis: \[ y=0 \] \[ x=1 \] Point: \[ (1,0) \] With \(x=2\): \[ y=2-1=1 \] Point: \[ (2,1) \] Third vertex on X-axis: \[ (2,0) \]

Step 3: Find area.
Base: \[ =2-1=1 \] Height: \[ =1 \] Area: \[ =\frac{1}{2}\times1\times1 \] \[ =\frac{1}{2} \]