Search any question & find its solution
Question:
Answered & Verified by Expert
In a rectangle $A B C D$, the coordinates of $A$ and $B$ are $(1,2)$ and $(3,6)$ respectively and some diameter of the circumscribing circle of $A B C D$ has equation $2 x-y+4=0$. Then the area of the rectangle is
Options:
Solution:
2462 Upvotes
Verified Answer
The correct answer is:
16
Slope of $\mathrm{AB}=\frac{4}{2}=2$
slope of $\mathrm{BC}=-\frac{1}{2}$
$\ell(\mathrm{AB})=\sqrt{4+16}=2 \cdot 5$
distance between $2 \mathrm{x}-\mathrm{y}+4=0 \quad \& \quad 2 \mathrm{x}-\mathrm{y}=0 \Rightarrow \frac{4}{\sqrt{5}}$
Area $=2 \sqrt{5} \cdot \frac{8}{\sqrt{5}}=16$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.