Question

a ray of light is reflected from a mirror such that the reflected ray is perpendicular to the original ray, as shown in the diagram. the point does not lie on the reflected ray. select the correct answer from each drop - down menu. the equation of the reflected ray is: y - x = 5, y + x = 5, -y + x = 6, y + x = 6, y - x = 6. c(1, 5) mirror b a reflected ray e d y - x = 4

Explanation:

Step1: Recall slope - intercept form

The equation of a line is \(y = mx + c\), and for the line \(y - x=4\) (or \(y=x + 4\)), the slope \(m_1 = 1\). If two lines are perpendicular, the product of their slopes \(m_1\times m_2=- 1\). So, the slope of a line perpendicular to \(y - x = 4\) is \(m_2=-1\).

Step2: Use point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(1,5)\) and \(m=-1\). Substituting these values, we get \(y - 5=-1(x - 1)\).

Step3: Simplify the equation

Expand the right - hand side: \(y - 5=-x + 1\). Then, rearrange the terms to get \(y+x=6\).

Answer:

\(y + x=6\)