Find the area of triangle with A(1,-4) and mid point of sides through

1.	Find the area of triangle with A(1,-4) and mid point of sides through being (2,-1)and (0,-1).
Answer» Let E be the midpoint of AB.{tex}\\therefore \\quad \\frac { x + 1 } { 2 } = 2{/tex}\xa0or x = 3and\xa0{tex}\\frac { y + ( - 4 ) } { 2 } = - 1{/tex} or, y = 2or, B(3, 2)Let F be the mid-point of AC.Then,{tex}0=\\frac{x_1+1}{2}{/tex}\xa0or\xa0{tex}x_1=-1{/tex}and {tex}\\frac { y _ { 1 } + ( - 4 ) } { 2 }{/tex}\xa0= -1 or, y1\xa0= 2or, C= (-1, 2)Now the co-ordinates are A(1, - 4), B(3,2), C (-1,2)Area of triangle{tex}= \\frac { 1 } { 2 } \\left[ x _ { 1 } \\left( y _ { 2 } - y _ { 3 } \\right) + x _ { 2 } \\left( y _ { 3 } - y _ { 1 } \\right) + x _ { 3 } \\left( y _ { 1 } - y _ { 2 } \\right) \\right]{/tex}{tex}= \\frac { 1 } { 2 } [ 1 ( 2 - 2 ) + 3 ( 2 + 4 ) - 1 ( - 4 - 2 ) ]{/tex}{tex}= \\frac { 1 } { 2 } [ 0 + 18 + 6 ]{/tex}= 12 sq units.

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