Question

solve it with steps by explanation​

Answer 1

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

Answer 2

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