Question

Find the area of triangle amn, where m and n
are the midpoints of the AB and AC
of triangle ABC where vertices are A(0,-1), B(2,1)
c(0,3).​

Answer 1

Step-by-step explanation:

Vertices of ΔABC are A(0,−1),B(2,1) and C(0,3)

Area of ΔABC=

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

Area of triangle ABC:

=

2

1

[0(1−3)+2(3+1)+0(−1−1)]

=

2

1

[0+2×4+0]=

2

1

×8=4 sq. units.

From figure: Points D, E and F are midpoints of sides BC, CA and AB respectively.

Find the coordinates of D, E and F

Coordinates of D

=(

2

2+0

,

2

1+3

)

=(1,2)

Coordinates of E

=(

2

0+0

,

2

3−1

)

=(0,1)

Coordinates of F

=(

2

0+2

,

2

−1+1

)

=(1,0)

Area of triangle DEF:

=

2

1

[1+0+1]

=1 sq. units

Therefore,

Ratio in the area of triangles ABC and DEF=

1

4

=4:1.