Question

Through the point (3,4) are drawn to straight line each inclined at 45 degree to the straight line x-y=2. Find their equations and also find the areas of triangle bounded by the three lines

Answer 1

Slope of line x - y = 2 is 1. This line makes an angle of 45 degrees with positive x-axis.

Let m1 and m2 be the slopes of the lines that make an angle of 45 degrees with x - y = 2

It is obvious that one line will be parallel to x-axis and the other parallel to the y-axis.

So, one line is x = 3 and the other y = 4

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

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

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

Therefore, the area of the triangle is 3$\sqrt{2}$ square units.