Question

The co-ordinates of the vertices of a triangle are (3, 1), (b, 4), and (1, a), and its centroid is (3, 4). Find the values of a and b.

Answer 1

Using the centroid formula:

centroid = `((x_1 + x_2 + x_3) / 3, (y_1 + y_2 + y_3) / 3)`

Here, the vertices are (3, 1), (b, 4), (1, a), and the centroid is (3, 4),

So `(3 + b + 1)/3 = 3 and (1 + 4 + a)/3 = 4`

Thus,

⇒ `(4 + b) / 3` = 3

4 + b = 9

∴ b = 5

⇒ `(5 + a) / 3` = 4

5 + a = 12

∴ a = 7

Hence, the values of a and b are (7, 5).