Question

The image of a point $A ( 3,8 )$ in the line $x + 3 y - 7 = 0$, is

• A. (–1, –4)
• B. (–3, –8)
• C. (1, –4)
• D. (3, 8)

Answer 1

Answer: (A)

(–1, –4)

Answer 2

Equation of the line passing through (3, 8) and perpendicular to $A ( 3,8 )$ be $A ^ { \prime } \left( x _ { 1 } , y _ { 1 } \right)$.

The point (1, 2) will be the midpoint of $A A ^ { \prime }$. $\frac { x _ { 1 } + 3 } { 2 } = 1$

⇒ $x _ { 1 } = - 1$ and $\frac { y _ { 1 } + 8 } { 2 } = 2$ ⇒ $y _ { 1 } = 4$ . Hence the image is

(–1, –4).C