UPSC NDA Math Model Paper 8

Given, the area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 square units.
We know that , area of a triangle with vertices (x1,y1),(x2,y2),(x3,y3) is given by
Area =

1

2

|

x1	y1	1
x2	y2	1
x3	y3	1

|
⇒ Area =

1

2

|

−3	0	1
3	0	1
0	k	1

|
⇒ Area =

1

2

[−3(0−k)−0+1(3k)]
⇒ Area = 3k
The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 square units.
⇒ 3k = 9
⇒ k = 3
Hence, If the area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 square units, then the value of k is 3.