Question

If the centroid of a triangle is (4,-2) and two of its vertices are (3,-2) and (5,2) then find the third vertex of the triangle

Answer 1

FORMULAE FOR CENTROID IS..

x=x1+x2+x3÷3

y=y1+y2+y3÷3

4=x+3+5÷3

x=8÷12

x=2/3

-2=y+(-2)+2

y=-2

Answer 2

The third vertex of the triangle is (4,-6).

Step-by-step explanation:

Centroid of a triangle is (4,-2) and two of its vertices are (3,-2) and (5,2).

We need to find the third vertex of the triangle.

Let third vertex of the triangle is (a,b).

Centroid of a triangle is

$Centroid =(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3})$

Using the formula, centroid of the triangle is

$Centroid =(\dfrac{3+5+a}{3},\dfrac{-2+2+b}{3})$

Centroid of a triangle is (4,-2).

$(4,-2) =(\dfrac{8+a}{3},\dfrac{b}{3})$

On comparing both sides we get

$\dfrac{8+a}{3}=4\Rightarrow 8+a=12\Rightarrow a=4$

$\dfrac{b}{3}=-2\Rightarrow b=-6$

Therefore, the third vertex of the triangle is (4,-6).

#Learn more

Find the centroid of the triangle whose vertices are (-2,3),(2,-1) ,(4,0)​.

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