Two lines are drawn through 3,4 each of which makes angle of 45∘ with the line x−y=2. Then area of the triangle formed by these lines is

# Two lines are drawn through $\left(3,4\right)$ each of which makes angle of ${45}^{\circ }$ with the line $x-y=2$. Then area of the triangle formed by these lines is

1. A

$9$

2. B

$\frac{9}{2}$

3. C

$2$

4. D

$\frac{2}{9}$

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### Solution:

The equation of lines are $y-{y}_{1}=\frac{m±tan\alpha }{1\mp mtan\alpha }\left(x-{x}_{1}\right)$

$⇒y-4=\frac{1±tan{45}^{\circ }}{1\mp tan{45}^{\circ }}\left(x-{x}_{1}\right)$

$⇒y-4=\frac{1±1}{1\mp 1}\left(x-3\right)$

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