Select the correct answer from each drop-down menu.
Diagram shows mirror AB with a midpoint C (1, 5). Two rays spans out from C. One is labeled y minus x equals 4 and it extends up and to the right through point D. Another is labeled reflected ray and it extends down and to the right through point E.
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.
The equation of the reflected ray is correct, but the blank space is incomplete. Could you please provide more context or information?
The equation of the reflected ray is (y - 5) - (x - 1) = 0. The point E does not lie on the reflected ray.
To find the equation of the reflected ray, we can use the information given in the diagram. The reflected ray is perpendicular to the original ray, which means their slopes are negative reciprocals of each other.
The equation of the original ray is given as "y - x = 4". To find the slope of this line, we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation "y - x = 4", we get "y = x + 4". Comparing this with the slope-intercept form, we can see that the slope (m) of the original ray is 1.
Since the reflected ray is perpendicular to the original ray, the slope of the reflected ray is the negative reciprocal of the slope of the original ray. Thus, the slope of the reflected ray is -1.
Now, let's find the equation of the reflected ray using the slope-intercept form. We know the point C (1, 5) lies on the reflected ray, so we can substitute these values into the equation.
Using the slope (m = -1) and the point-slope form of a linear equation (y - y1 = m(x - x1)), we get:
y - 5 = -1(x - 1)
y - 5 = -x + 1
y = -x + 6
Therefore, the equation of the reflected ray is "y = -x + 6".
The point that does not lie on the reflected ray is not mentioned in the question, so we cannot determine which point that would be. Please provide more information or specify the point you are referring to.