Question

The points $A(1,3)$and $C(5,1)$are the opposite vertices of rectangle. The equation of line passing through other two vertices and of gradient $2$, is

• A. $2x+y-8=0$
• B. $2x-y-4=0$
• C. $2x-y+4=0$
• D. $2x+y+7=0$

Answer 1

The correct option is B

$2x-y-4=0$

Find the equation of the line based on given information

Given, $A(1,3)$ and $C(5,1)$are the opposite vertices.

The midpoint of $AC=\left(\frac{1+5}{2},\frac{3+1}{2}\right)$

$=(3,2)$

We know that the diagonals of a rectangle bisect each other.

Therefore, the required line will pass through $(3,2)$.

The slope of the line $=2$

Since the equation of a line passing through point $\left(x_1,y_1\right)$is given as,

$(y-y_1)=m(x-x_1)$

$\Rightarrow$ $(y-2)=2(x-3)$

$\Rightarrow y-2-2x+6=0$

$\Rightarrow$ $2x-y-4=0$

Hence option $\left(B\right)$, $2x-y-4=0$ is the correct answer.