Question

One vertex of a square $ABCD$ is $A(-1,1)$ and the equation of diagonal $BD$ is $3x+y-8=0.$ Then

• A. $C\equiv (-7,-1)$
• B. $C\equiv (5,3)$
• C. $\text{Area of square}=40\text{sq. units}$
• D. $\text{Area of square}=20\text{sq. units}$

Answer 1

Answer: (B), (D)

The correct options are
B $C\equiv (5,3)$
D $\text{Area of square}=20\text{sq. units}$


Equation of $BD$ is $3x+y-8=0$

In a square, the diagonals bisect each other perpendicularly. So,
$C(h,k)$ is the image of $A$ with respect to line $BD.$
$\Rightarrow \frac{h+1}{3}=\frac{k-1}{1}=-\frac{2(-3+1-8)}{10}\Rightarrow (h,k)=(5,3)\Rightarrow AC=\sqrt{36+4}=2\sqrt{10}$

$\text{Area of square}=\frac{1}{2}(AC{)}^2=20\text{sq. units}$