Question

The area of the triangle formed by the points (1,2),(2,3),(x,4)is 40 sq. unit,then x is

Answer 1

The value of x is (- 77)

Step-by-step explanation:

The given points are (1, 2), (2, 3) and (x, 4)

Then the area of the triangle formed by these points be

| 1 2 1 |

= 1/2 * | 2 3 1 | sq. units

| x 4 1 |

= 1/2 * [1 (3 - 4) - 2 (2 - x) + 1 (8 - 3x)] sq. units [ expanding along the first row ]

= 1/2 * (- 1 - 4 + 2x + 8 - 3x) sq. units

= 1/2 * (3 - x) sq. units

According to the question,

1/2 * (3 - x) = 40

or, 3 - x = 80

or, x - 3 = - 80

or, x = - 77

Therefore the value of x is (- 77).