Question

find the area of triangle ABC with the coordinates of a as( 1 ,- 4) and the coordinates of the midpoints of sides ab and ac respectively are( 2, - 1) and (0 ,- 1 )​

Answer 1

Heya

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Area of Trangle having co-ordinates of vertices as ( x1 , y1 ) , ( x2 , y2 ) And

( x3 , y3 ) is

1/2{ x1(y2-y3)-x2(y1-y3)+x3(y1-y2)}

Let the co-ordinates of B be ( a,b ). And Co-ordinates of C be ( c,d )

Using Mid point theorem.

2 = a + 1 /2 And -1 =( b -4 )/2

a = 4 - 1 And b = -2 +4

a = 3 And b = 2

0 =( 1 + c ) /2 And -1 = ( -4+d)/2

c = -1 And d = 2

It's area is

1/2 { 1(2-2) -3(-4-2) -1(-4 -2)

=>

1/2( 6 + 18 )

=>

24/2

=>

12sq units