Problem Solving

Problem Solving

4. A ray of light travels from the left to along the line x + y = 1 and reflects off the x axis. Write the equation for the reflected ray.

Draw x-y coordinate axes and sketch the ray equation x + y = 1 and the reflection off the x-axis. The reflected ray will be perpendicular to the initial ray.

The slopes of two perpendicular lines are related by: m1 = -1/m2.

    Rewrite the first equation to see the slope of the line:        y = -x + 1

   The slope is -1. The slope of the second line is then: m2 = -1/(-1) = 1.

    We have:         y = x + b

   We need a data point to solve for b. Use the point where the line bounces off the x-axis.

        (1, 0)

        0 = 1 + b            b = -1

     Then:    y = x – 1

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