Question

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

Answer 1

Step-by-step explanation:

y−x=0....(1)

x+y=...(2)

x−k=0...(3)

The point of intersection of lines (1) and (2) is given by

x=0 and y=0 

The point of intersection of lines (2) and (3) is given by

x=k and y=−k

The point of intersection of lines(3) and (1) is given by

x=k and y=k

Thus, the vertices of the triangle formed by the three given lines are (0,0),(k,−k), and (k,k)

We know that the area of the triangle whose vertices are (x1,y1),(x2,y2), and (x3,y3) is 21∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣ 

Therefore, area of the triangle formed by the three given lines, 

=21∣0(−k−k)+k(k−0)+k(0+k)∣square unts

=21∣∣∣k2+k2∣