SSC CGL 2025 PYQ — Question 57

The correct answer is option 4 i.e.  y = x + 2.

Midpoint $(M)= \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

For (2, 8) and (6, 4): $M = \left( \frac{2+6}{2}, \frac{8+4}{2} \right)$ = (8/2, 12/2) = (4, 6)

Slope of line through two points $(m) = \frac{y_2 - y_1}{x_2 - x_1}= \frac{4-8}{6-2} = -\frac{4}{4} = -1$

Perpendicular slope $= -\frac{1}{m} = -\frac{1}{-1} = 1$

Equation of line (point-slope form): y - y₁ = m(x - x₁)

Using (4, 6) and m = 1: y - 6 = 1(x - 4)

⇒ y = x + 2