Question

find the area of the triangle ABC with A(1,-4) and mid point of side through A being (2,-1)and (0,-1).
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Answer 1

Answer:

Find the area of the triangle ABC with A(1,−4) and mid points of sides through A being (2,−1) and (0,−1)

A(1,-4)

Considering,

AB(2,−1)

AC(0,−1)

Let B(x

1

,y

1

)

(

2

x

1

+1

,

2

y

1

−4

)=(2,−1)

x

1

=3,y

1

=2

B(3,2)

Let C(x

2

,y

2

)

(

2

x

2

+1

,

2

y

2

−4

)=(0,−1)

x

2

=−1,y

2

=2

C(−1,2)

Area=

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

=

2

1

[3(2+4)+(−1)(−4−2)+1(2−2)]

=

2

1

[18+6+0]

=

2

24

Area of triangle =12 sq. units

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