Question

the vertices of a triangle ABC and given by A(2,3) and B(-2,1) and its centroid is G(1,2/3).find the coordinates of the third vertex C Of the triangle ABC

Answer 1

Answer:

Step-by-step explanation:

Hope it help

Answer 2

The coordinates of the third vertex C Of the triangle ABC is (3,-2)

Step-by-step explanation:

We are given the following information:

The vertices of triangle ABC are A(2,3) and B(-2,1).

The centroid of the triangle is

$G(1,\dfrac{2}{3})$

• Centroid is defined as the point where the three medians of the triangle meet.

Formula:

$G(x,y) = \bigg(\dfrac{x_1+y_1+z_1}{3},\dfrac{x_2+y_2+z_2}{3}\bigg)$

Let $(z_1,z_2)$ be the coordinates of vertex C of triangle ABC.

Putting the values, we get,

$G(1,\dfrac{2}{3}) = \bigg(\dfrac{2+(-2)+z_1}{3},\dfrac{3+1+z_2}{3}\bigg)\\\\\Rightarrow 1 = \dfrac{2+(-2)+z_1}{3}\\z_1 = 3\\\\\Rightarrow \dfrac{2}{3} = \dfrac{3+1+z_2}{3}\\\\z_2 = -2$

Thus, the coordinates of the third vertex C Of the triangle ABC is (3,-2)

#Learnmore

Two vertices of a triangle ABC are given by A 6,4) and b - 2, 2 and its centroid is G 3, 4 find the coordinates of the third vertex c of triangle ABC

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