Question

Two lines are drawn from the point $(3,4)$. If the lines make angle ${45}^{\circ }$ with the line $x-y=2$ then area of triangle formed by the lines is -

• A. $9$
• B. $\frac{9}{2}$
• C. $2$
• D. $\frac{2}{9}$

Answer 1

The correct option is B $\frac{9}{2}$

$\begin{array}{c}d=\frac{|3-4-2|}{\sqrt{1^2+1^2}}=\frac{3}{\sqrt{2}}\\ \tan {45}^0=\frac{2d}{base}\Rightarrow d=\frac{base}{2}\\ area=\frac{1}{2}\times base\times d=d\times d=\frac{9}{2}\end{array}$