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

Solution (By Examveda Team)

Slope of line PR
$$\eqalign{ & \Rightarrow {m_1} = \frac{{0 - 2}}{{ - 2 - 4}} \cr & \Rightarrow {m_1} = \frac{{ - 2}}{{ - 6}} \cr & \Rightarrow {m_1} = \frac{1}{3} \cr} $$
∴ 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