Question

S1 : If (0, 3), (1,1) and (–1, 2) be the mid points of the sides of a triangle, then centroid of the original triangle is (0, 2)

Answer 1

Step-by-step explanation:

Let the vertices be (x

1

,y

1

),(x

2

,y

2

),(x

3

,y

3

)

Centroid of △=(

3

x

1

+x

2

+x

3

,

3

y

1

+y

2

+y

3

)

Midpoints of triangle are (

2

x

1

+x

2

,

2

y

1

+y

2

),(

2

x

2

+x

3

,

2

y

2

+y

3

)(

2

x

1

+x

3

,

2

y

1

+y

3

)

Hence centroid is

3

2

x

1

+x

2

+

2

x

2

+x

3

+

2

x

1

+x

3

,

3

2

y

1

+y

2

+

2

y

2

+y

3

+

2

y

1

+y

3

=

3

x

1

+x

2

+x

3

,

3

y

1

+y

2

+y

3

We observe that △ formed by midpoints also has same centroid.

∴ Centroid of original △=(

3

0+2+−2

,

3

3+2+1

)

=(0,2)

So both assertion and reason are explained