Question

1. Centroid of a triangle whose midpoints of sides
are A(1, 2), B(2, -3) and C(6, 7) is​

Answer 1

Given Mid Points of sides are

A ( 1,2)

B ( 2, - 3)

C ( 6, 7)

Let the triangle be PQR

where, A, B, C are the mid points of PQ, QR, PR respectively.

Now,

P = A + C - B

P = (1 + 6 - 2, 2 + 7 + 3).

P = ( 5, 12)

Q = A + B - C

Q = ( 1 + 2 - 6, 2 - 3 - 7)

Q = ( - 3, - 8)

R = B + C - A

R = ( 2 + 6 - 1, - 3 + 7 - 2)

R = ( 7, 2)

Now we have vertices of the triangle,

Centroid = { ( 5 - 3 + 7) / 3, (12 - 8 + 2)/3}

G = { 3, 2}

Or, The centroid of the triangle formed by the mid points of sides is same as the centroid of the triangle.

So,

A ( 1,2)

B ( 2, - 3)

C ( 6, 7)

G = { (1 + 2 + 6 )/ 3, ( 2- 3 + 7) /3}

G = { 3, 2}

Therefore, The centroid of the triangle is (3, 2).

Answer 2

Answer:

The centroid of a triangle is (2,3).

Thank you

Step-by-step explanation: