Question

30] 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​

Answer 1

Answer:

$area \: of \: triangle \: = \frac{9}{2} {cm}^{2}$✔✔

Step-by-step explanation:

Slope of line x-y=2 that is 1

This line makes angle=45 degree with x-axis

Let M1 and M2 be the slope of the lines that makes an angle of 45 degree with x-y=2.

It is obivious that one line is parallel to x-axis and other to y-axis so one line of x=3 and y=4 .

The line x=3 will meet the line x-y=2 at y=1.

The line y=4 at the line x=3 will meet the line x-y=2 at x=6.

Therefore, the arms of right angled triangle are of length of 3 units each therefore, the area of triangle is

$\frac{1}{2} \times 3 \times 3 \\ =\frac{9}{2}cm^2$

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