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
options:
y - x = 6
y + x = 6

• y + x = 6

y + x = 5
y - x = 5
. the point
does not lie on the reflected ray.

Explanation:

Step1: Find slope of incident ray

The incident ray has equation $y - x = 4$, rewritten as $y = x + 4$. Its slope $m_1 = 1$.

Step2: Find slope of reflected ray

Since incident and reflected rays are perpendicular, $m_1 \times m_2 = -1$. Substitute $m_1=1$:
$1 \times m_2 = -1 \implies m_2 = -1$

Step3: Find equation of reflected ray

Reflected ray passes through $C(1,5)$. Use point-slope form $y - y_1 = m(x - x_1)$:
$y - 5 = -1(x - 1)$
Simplify: $y - 5 = -x + 1 \implies y + x = 6$

Step4: Verify points (example check)

Take $y+x=6$:

• For $(2,4)$: $2+4=6$, lies on ray.
• For $(3,4)$: $3+4=7

eq6$, does not lie on ray.

Answer:

The equation of the reflected ray is $\boldsymbol{y + x = 6}$.
A point that does not lie on the reflected ray (e.g., $\boldsymbol{(3, 4)}$) (any point not satisfying $y+x=6$ is valid)