Question

2 vertices of triangle ABC are A(6,4)amd B(-2,2).if the centroid is G(3,4).Find the third vertex of the triangle

Answer 1

Answer:

2 vertices of triangle ABC are A(6,4)amd B(-2,2).if the centroid is G(3,4).Find the third vertex of the triangle

Answer: (5, 6)

Step-by-step explanation:

Solution:

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

Two vertices of triangle ABC are A(6,4)amd B(-2,2).

Given A (6, 4) and B (-2, 2) & centroid G (3, 4)

As we know that

centroid of triangle = $\frac{x_{1} + x_{2}+ x_{3}}{3} , \frac{y_{1} + y_{2}+ y_{3}}{3}$

Hence, x-coordinate of centroid of triangle

$\frac{x_{1} + x_{2}+ x_{3}}{3} = 3$

$\frac{6-2+x}{3} = 3$

⇒ 6 -2 + x = 9

⇒ x = 9 - 4

⇒ x = 5

and again y-coordinate of centroid of triangle,

$\frac{y_{1} + y_{2}+ y_{3}}{3} = 4$

⇒ $\frac{4+2+y}{3} = 4$

⇒ 6 + y = 12

⇒ y = 12 - 6 = 6

Therefore third vertex of triangle will be C (5, 6)

Answer 2

Two vertices of triangle ABC are A (6,4) B(-2,2) its centroid is G(3,4). The coordinates of third vertex C of triangle ABC is C(5,6)

Stepwise explanation is given below:

- As per the question says that the vertices of traingle ABC are A(6,4) , B(-2,2) and its centroid is G(3,4).

- The centroid of the circle is given by

C=[(x1 + x2 + x3)/3]=3 ,[(y1+y2+y3)/3]=4

- To find the x3, put the values of the coordinates

Here [6+(-2)+x]/3=3

(x+4)/3=3

x+4=9

x=5

- Similarly, to find the coordinate of y3

(4+2+y)/3=4

(6+y)=12

Y=6

- So, the other vertex of the triangle is C(5,6)