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 (a) 9 (b) `9/2` (c) 2 (d) `2/9`

Options

A. 9
B. `9//2`
C. 2
D. `2//9`

Answer

B

Explanation

The equation of lines are `y - y_(1) = (m +- tan alpha)/(1 +- m tan alpha) (x-x_(1))`
`rArr y - 4 =(1+- tan 45^(@))/(1+-tan 45^(@)) (x-x_(1))`
`rArr y - 4 = (1+-1)/(1+-1) (x-3)`
`rArr y = 4` or `x = 3`
Hence, the lines which make the triangle are `x - y = 2, x = 3` and `y = 4`.
THe intersection points of these lines are `(6,4),(3,1)` and (3,4).
`:. Delta =(1)/(2) |6(-3)+3(0)+3(3)| =(9)/(2)`