Question

In a triangle ABC,A=(5,8) D is the mid point of side BC and D=(2,-1) find the centroid of ABC​

Answer 1

The coordinates of the centroid are (3,2).

Step-by-step explanation:

In a triangle, Δ ABC, the median through the vertex A is AD, where D is the midpoint of BC.

Now, given that the coordinates of A and D are (5,8) and (2,-1) respectively.

We know that at the point centroid all the medians of a triangle breaks in a 2 : 1 ratio.

We have to find the centroid.

Hence, from the formula of coordinate geometry, we can write the coordinates of the centroid will be $(\frac{2 \times 2 + 5 \times 1 }{2 + 1}, \frac{2\times (-1) + 8 \times 1}{2 + 1}) = (3,2)$ (Answer)

Answer 2

Centroid (3, 2)

Step-by-step explanation:

In Δ ABC, AD is the the median through the vertex A and D is the midpoint of BC.

Coordinates of A and D are (5,8) and (2,-1) respectively.

We know that at the centroid, the medians of all 3 sides of a triangle will intersect to cut each other in the ratio 2 : 1.

To find the centroid, using the formula of coordinate geometry, the coordinates of the centroid will be:

[ (2*2 + 5 *1) / 2 + 1 , (2*-1 + 8 *1) / 2 + 1 ] =  (3, 2)