Question

4. Find the area of the triangle formed by the lines :
y - x = 0, x + y = 0 and x- k = 0​

Answer 1

Answer:

Equation of line 1,L1→y−x=0⇒x=y→(1)

Equation of line 2,L2→x+y=0⇒x=−y→(2)

Equation of line 3,L3→x−k=0⇒x=k→(3)

Now, if we draw these lines, it will form a triangle with vertices, (0,0),(k,k),(k,−k).

Please refer to video for the diagram.

Now, from the diagram, we can see that,

Base of triangle =2k

Altitude of triangle =k

So, Area of triangle = 1/2*base*height

∴ Area =12⋅2k⋅k=k2 square units