SSC IMD SA 2017 – Question 40

What is the reflection of the point (-2, 6) in the line x = -1?

• (-2 , -8)
• (2 , 6)
• (0 , 6)
• (-2 , 8)

Detailed Explanation:

We need to find the reflection of the point $(-2, 6)$ across the vertical line $x = -1$.

Step-by-step Solution:

1. Let the original point be $P(x_1, y_1) = (-2, 6)$ and the reflected image point be $P'(x’, y’)$.
2. Properties of reflection across a vertical line $x = c$:
   • The line $x = c$ is parallel to the y-axis, so the y-coordinate remains unchanged:$$y’ = y_1 = 6$$
   • The line $x = c$ is the perpendicular bisector of the segment connecting $P$ and $P’$. Therefore, the midpoint of the x-coordinates must lie on $x = c$:$$\frac{x_1 + x’}{2} = c \implies x’ = 2c – x_1$$
3. Substitute $c = -1$ and $x_1 = -2$:$$x’ = 2(-1) – (-2) = -2 + 2 = 0$$
4. Therefore, the coordinates of the reflected point are:$$P'(x’, y’) = (0, 6)$$

Hence, the correct option is c) (0 , 6).