Question

If (x1, y1) = (2, 3); x2= 3 and y3 = -2 and G is (0,0), Find y2 and x3.​

Answer 1

Answer:

x3 = -5 ; y2 = - 1

Step-by-step explanation:

We know,

G(x, y) = ( (x1+x2+x3)/3, (y1+y2+y3)/3 )

Substituting the values,

=> (0,0) = ( (2+3+x3)/3 , (3+y2-2)/3 )

=> (0,0) = ( (5+x3)/3, (1+y2)/3 )

=> 0 = (5+x3)/3 & 0 = (1+y2)/3

=> 0 = 5+x3 & 0 = 1 + y2

=> - 5 = x3 & - 1 = y2

Answer 2

Question :

The coordinates of a triangle are (x₁ , y₁) = (2 , 3) ; x₂ = 3 and y₃ = -2. The coordinates of the centroid are (0 , 0) Then Find y₂ and x₃.

Given :

• (x₁ , y₁) = (2 , 3) ; (x₂ , y₂) = (3 , y₂)

• (x₃ , y₃) = (x₃ , -2)

• G = (0,0)

To Find :

• y₂ and x₃

Knowledge required :

If the three vertices of a triangle are (x₁ , y₁) , (x₂ , y₂) and (x₃ , y₃) then the coordinates of centroid are given by ,

$\large{ \boxed{ \rm{G = \bigg(\dfrac{x_1+x_2+x_3}{3} , \dfrac{y_1 + y_2 + y_3}{3}\bigg)}}}$

Solution :

We have ,

• x₁ = 2 , x₂ = 3 , x₃ = x₃
• y₁ = 3 , y₂ = y₂ , y₃ = -2

By susbstituting the values in the formula we get ;

$\\ \implies \rm \: (0,0)= \bigg(\dfrac{2+3+x_3}{3} , \dfrac{ 3+ y_2 + - 2}{3}\bigg)$

• Equating x-coordinates we get ;

$\\ \implies \rm \: 0 = \dfrac{2+3+x_3}{3} \\ \\ \\ \implies \rm \: 0 \times 3= 2 + 3 + x_3 \\ \\ \\ \implies \rm \: 0 = 5 + x_3 \\ \\ \\ \implies \underline {\boxed {\bf{ \pink{x_3 = - 5}}}}$

• Now by equating y-coordinates we get ;

$\\ \implies \rm \: 0= \dfrac{3 + y_2 + - 2}{3} \\ \\ \\ \implies \rm \: 0 \times 3= 3 + ( - 2) + y_2 \\ \\ \\ \implies \rm \: 0 = 3 - 2 + y_2 \\ \\ \\ \implies \rm \: 0 = 1 + y_2 \\ \\ \\ \implies \underline {\boxed{ \bf {\pink{y_2 = - 1}}}}$

Hence ,

• x₃ = -5
• y₂ = -1