Question

Through the point $(3,4)$ are drawn two straight lines each inclined at ${45}^o$ to the straight line $x-y=2$. find their equations and also find the area of triangle bounded by the three lines.

Answer 1

Slope of line $x-y=2$ is $1$. This line makes an angle ${45}^{\circ }$ with positive x-axis.

Let $m1$ and $m2$ be the slopes of the lines that make an angle ${45}^{\circ }$ with $x-y=2$

It is obvious that one line is parallel to x-axis and the other is parallel to 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