 Hello and welcome to the session. Let us discuss the following question. It says find the area of the Triangle formed by the lines y minus x is equal to 0 x plus y is equal to 0 x minus k is equal to 0 What is we need to know the formula for area of triangle having vertices 1 y 1 x 2 y 2 and x 3 y 3 and the formula is given by 1 by 2 into mod of x 1 into y 2 minus y 3 plus x 2 into y 3 minus y 1 plus x 3 into y 1 minus y 2 So this is the key idea Let us now proceed on with the solution. We have to find the area of the Triangle formed by these three lines for that we first need to find the vertices of the Triangle and That vertices are actually the point of intersection of these three lines. So the lines given to us are Y minus x is equal to 0 let's call this as 1 Second line given to us is y plus x is equal to 0 Let's call this as 2 and the third line given to us is x minus k is equal to 0. Let's call this as 3 Now to find the point of intersection of these three lines will solve these equations For x and y So we first solve 1 and 2 Solving 1 and 2 gives us x is equal to 0 and y is equal to 0 so the one vertex of Triangle is 0 0 and solving 2 and 3 gives us x is equal to k from 3 we have x is equal to k and From 2 we have y is equal to minus x. So this implies y is equal to minus k so The second vertex of the Triangle is k minus k and then we solve 1 and 3 Solving 1 and 3 gives us x is equal to k from 3 and from 1 we have y is equal to x So that gives us y is equal to k since x is equal to k So third vertex of the Triangle is kk Now we find area of Triangle having vertices 0 0 k minus k and Kk it is equal to 1 by 2 into mod of x1 that is 0 into y2 minus y3 Now y2 is minus k y3 is k plus x2 where x2 is k into y3 minus y1 where y3 is k and y1 is 0 plus 3 here x3 is k Into y1 minus y2 where y1 is 0 Minus y2 y2 is minus k now. This is equal to 1 by 2 into k square Plus k square. So this is equal to 1 by 2 into 2 k square This is equal to k square hence the area of Triangle having vertices 0 0 k minus k and kk is k square Square units and the answer is k square square units. So this completes the question Goodbye and take care