Question

If P(2,1), Q(-2,2) and R(-1,4) are the midpoints of sides Traingle ABC, find the vertices of triangle ABC.

Answer 1

Answer:

Let P(1, 1),Q(2,−3), R(3, 4) be the mid-points of sides AB, BC and CA respectively of triangle ABC.

Let A(x

1

,y

1

),B(x

2

,y

2

) and C(x

3

,y

3

) be the vertices of triangle ABC.

Then, P is the mid point of AB

⇒

2

x

1

+x

2

=1,

2

y

1

+y

2

=1

⇒x

1

+x

2

=2andy

1

+y

2

=2 ..(1)

Q is the mid point of BC

⇒

2

x

2

+x

3

=2,

2

y

2

+y

3

=−3

⇒

2

x

2

+x

3

=4and

2

y

2

+y

3

=−3

⇒x

2

+x

3

=4andy

2

+y

3

=−6 ..(2)

R is the mid point of AC

⇒x

1

+x

3

=6andy

1

+y

3

=8 ..3)

From (1), (2) and (3) we get

(x

1

,y

1

)≡(2,8),(x

2

,y

2

)≡(0,−6)

and (x

3

,y

3

)≡(4,0)

Then the coordinates of the centroid

=(

3

x

1

+x

2

+x

3

,

3

y

1

+y

2

+y

3

)

=(

3

2+0+4

,

3

8−6+0

)=(2,

3

2

Answer 2

Answer:

Step-by-step explanation: