Question

The points $A(1,3)$ and $(5,1)$ are opposite vertices of a rectangle ABCD. If the slope of BD is $2$, then its equation is given by

• A. $2x+y-4=0$
• B. $2x-y-4=0$
• C. $2x+y+7=0$
• D. $2x+y-7=0$

Answer 1

The correct option is A $2x+y-4=0$

We know the diagonals of a rectangle intersects at a point.

Here diagonals are $AC$ and $BD$.

We know that mid-point of any diagonal is the intersection point.

Now, intersection point is $(\frac{1+5}{2},\frac{1+3}{2})=(3,2)$

We know that any point on the line, is a solution of the line and vice-versa.

Given slope of $BD$ is $m=2$.

Now take $y=2,x=3$

$\Rightarrow 2=2\left(3\right)+c$

$\Rightarrow c=2-6=-4$

So, the equation of the line is $y=2x-4$

This is further equal to $2x-y-4=0$.