Question

$A(-3,4),B(5,4)$ are two vertices of a rectangle ABCD and $4y=x+7$ is a diameter of the circle circumscribing ABCD. The width of the rectangle is

• A. $8$
• B. $6$
• C. $4$
• D. $2$

Answer 1

The correct option is C $4$

The midpoint of side $AB$ of the rectangle has coordinates $E:$ $(\frac{-3+5}{2},\frac{4+4}{2})=(1,4)$.
The equation of $AB$ is $y=4$. Hence, equation of line passing through $E$ and perpendicular to $AB$ is $x=1$.
$x=1$ will pass through the center. Also, the equation of one diameter is $4y=x+7$. Hence, coordinates of center are point of intersection of $x=1$ and $4y=x+7$.
We get the coordinates of center $O$ as $(1,2)$.
Width of rectangle is $2OE=2\times 2=4$