Question

The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2). What is the equation of the diagonal BD?

• (A) 2x + y = 0
• (B) 2x - y = 0
• (C) x + 2y = 0
• (D) x - 2y = 0

Answer 1

The Correct Option is A

Explanation:
Concept:The equation of a line passing through the point $(x_1,y_1)$ and having the slope ' $m$ ' is given as:$y-y_1=m\cdot (x-x_1)$Given: The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2).So, the diagonal AC passes through the origin,As we know that, the slope of the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ is: $m=\frac{y_2-y_1}{x_2-x_1}$The slope of line $AC$ is given by$\frac{2-0}{4-0}=\frac{1}{2}$In square $ABCD$, the diagonals $AC$ and $BD$ are perpendicular to each other.$\Rightarrow \text{ Slope of }AC\times \text{ slope of }BD=-1$So, the slope of BD is - 2 .As we know that, the equation of a line passing through the point $(x_1,y_1)$ and having the slope ' $m$ ' is given as:$y-y_1=m\cdot (x-x_1)$The equation of $BD$ whose slope is - 2 and passes through origin is given by:$y-0=(-2)\cdot (x-0)$$\Rightarrow 2x+y=0$Hence, the correct option is (A).