Two Vertices of a triangle ABC are given by A(6,4) and B(-2,2), and its centroid is G(3,4) Find coordinates - Maths - Coordinate Geometry

Question

Two Vertices of a triangle ABC are given by A(6,4) and B(-2,2),
and its centroid is G(3,4) Find coordinates of the third vertex C
of Triangle ABC

Gursheen kaur. · Accepted Answer

Given: The coordinates of two vertices of a triangle ABC are A(6, 4), B(-2, 2) and the coordinates of the centroid is

G(3,4).

Let the coordinate of the third vertex of the triangle be C(x, y).

⇒ Coordinates of G = $(\frac{6 - 2 + x}{3}, \frac{4 + 2 + y}{3}) = (\frac{4 + x}{3}, \frac{6 + y}{3})$

$\Rightarrow (3, 4) = (\frac{4 + x}{3}, \frac{6 + y}{3}) \Rightarrow 3 = \frac{4 + x}{3} a n d 4 = \frac{6 + y}{3}$

⇒ 4+x = 9 and 6 + y = 12

⇒ x = 9 - 4 = 5 and y = 12 - 6 =6

Hence, the required coordinate of the third vertex of the triangle is C(5, 6).

Two Vertices of a triangle ABC are given by A(6,4) and B(-2,2), and its centroid is G(3,4). Find coordinates of the third vertex C of Triangle ABC.