Question

find the area of the triangle whose vertices are (1,5)( 2,3) and (- 2, - 11) ​

Answer 1

area of triangle = -11

refer to the attachment

Answer 2

HEY LEARNER ,

HERE IS YOUR ANSWER,

Area of the triangle in determinant form = $\left[\begin{array}{ccc}x1&y1&1\\x2&y2&1\\x2&y3&1\end{array}\right]$

Area of the triangle = $\frac{1}{2}$ [ x1 ( y2 - y3 ) + x2 ( y3 - y3 ) + x3 ( y1 - y2 )]

Let the given points be A( 1,5 ) , B ( 2,3 ) and C ( -2,-11 )

Area =1/2 [ 1 ( 3+11 ) + 2 (-11-5) - 2 (5-3) ]

        =1/2 [ 14 + 2 x (-16) - 4 ]

        = 1/2 [14 - 32 -4]

        = 1/3[14 - 36]

        = -11sq.units

Since area cannot be negative, area of triangle becomes 11 sq.units.

HOPE IT HELPS U!!!