Question

If the area of the triangle formed by the points (x, 2x), (−2, 6)  and (3, 1) is 5 square units , then x =

Options

• \[\frac{2}{3}\]

   

• \[\frac{3}{5}\]

   

• 3

• 5

Answer 1

We have the co-ordinates of the vertices of the triangle as A (x , 2x) ; B (-2 , 6) ; C ( 3 , 1) which has an area of 5 sq.units.

In general if `A (x_1 ,y_1 ) ; B (x_2 ,y_2) ; C (x_3 , y_3)`  are non-collinear points then area of the triangle formed is given by-,

`"ar"(ΔABC ) = 1/2 |x_1(y_2 -y_3) + x_2 (y_3 - y_1 ) + x_3 (y_1 - y_2 )|`

So,

`5 = 1/2 |x(6-1)-2(1-2x)+3(2x - 6)|`

`5 = 1/2|15x - 20|`

Simplify the modulus function to get,

`3x - 4 = +-2`

         `x = (4+-2)/3`

Therefore,

`x =2 , 2/3`