P(4, 2) and R(-2, 0) are vertices of a rhombus PQRS. What is the equation of diagonal QS?

Answer: Option B

Slope of line PR
$$\begin{array}{rl}& \Rightarrow m_1=\frac{0-2}{-2-4}\\ & \Rightarrow m_1=\frac{-2}{-6}\\ & \Rightarrow m_1=\frac{1}{3}\end{array}$$
∴ Slope of line QS = -3 = m₂ {As it is perpendicular to PR}
Coordinates of point O
$$\Rightarrow \left[\frac{-2+4}{2},\frac{2+0}{2}\right]\Rightarrow \left(1,1\right)$$
∴ Equation of line QS which passes through point O(1, 1)
⇒ y - 1 = m₂(x - 1)
⇒ y - 1 = -3(x - 1)
⇒ y - 1 = -3x + 3
⇒ 3x + y = 4