Question

The graphs of functions f(x) and g(x) = f(x) + k are shown below:

k=____
​

Answer 1

`\red{Centroid(G)= \big(2,(2)/(3)\big)}`

`\green{\begin{gathered}The\: coordinates \: of \\ the \: mid\:point \:of \: the \: sides \\of\:a\:triangle\:are\\ (1,1),(2,-3)\:and\:(3,4)\end{gathered}}`

`\orange{\begin{gathered}x_(1)=1,y_(1)=1;\\x_(2)=2,y_(2)=-3;\\x_(3)=3,y_(3)=4\end{gathered}}`

`\blue{\begin{gathered}Now,\\Centroid (G)=\big((x_(1)+x_(2)+x_(3))/(3),(y_(1)+y_(2)+y_(3))/(3)\big)\end{gathered}}`

`\red{\begin{gathered}=\big((1+2+3)/(3),(1-3+4)/(3)\big)\\=\big((6)/(3),(2)/(3)\big)\\=\big(2,(2)/(3)\big)\end{gathered}}`

Therefore,

`\pink{Centroid(G)= \big(2,(2)/(3)\big)}`