Question

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

Answer 1

Solution :

We have ,

x₁ = 2 , x₂ = 3 , x₃ = x₃

y₁ = 3 , y₂ = y₂ , y₃ = -2

By susbstituting the values in the formula we get ;

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

• Equating x-coordinates we get ;

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

• Now by equating y-coordinates we get ;

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

Hence ,

x₃ = -5

y₂ = -1