Question

select the correct answer from each drop - down menu.
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 equation of the reflected ray is. the point does not lie on the reflected ray.

Explanation:

Step1: Find the slope of the original ray

The equation of the original ray is \(y - x=4\), which can be rewritten as \(y=x + 4\). The slope \(m_1\) of the line \(y=x + 4\) is \(1\).

Step2: Determine the slope of the reflected ray

Since the reflected ray is perpendicular to the original ray, if the slope of the original ray is \(m_1\) and the slope of the reflected ray is \(m_2\), then \(m_1\times m_2=- 1\). Given \(m_1 = 1\), we get \(m_2=-1\).

Step3: Use the point - slope form to find the equation of the reflected ray

The line passes through the point \(C(1,5)\) and has a slope \(m=-1\). The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(1,5)\) and \(m=-1\).
Substitute into the formula: \(y - 5=-1(x - 1)\)
Expand: \(y-5=-x + 1\)
Rearrange: \(y+x=6\)

Step4: Check which point does not lie on the line \(y + x=6\)

For the line \(y+x=6\), we can check by substituting values.
Let's assume we have some points (not given in the problem, but based on the equation)
If \(x = 0\), then \(y=6\); if \(y = 0\), then \(x=6\)

Answer:

The equation of the reflected ray is \(y + x=6\).