Question

Find the centroid of triangle PQR whose vertices are P(1,1) ,Q(2,2) ,R(-3,-3)​

Answer 1

Step-by-step explanation:

\begin{gathered}\boxed{\begin{minipage}{11.44cm}\textsf{If the coordinates of the vertices of a triangle are \ $(x_1,\ y_1),\ (x_2,\ y_2)$ \ and \ $(x_3,\ y_3),$}\\ \\ \textsf{then the coordinates of the centroid of the triangle will be,}\\ \\ \begin{center}\large \text{$\left(\dfrac{x_1+x_2+x_3}{3},\ \dfrac{y_1+y_2+y_3}{3}\right)$}\end{center}\end{minipage}}\end{gathered}

Coordinates of three vertices of ΔPQR are given.

\begin{gathered}\mapsto\ P(1, 1)\\ \\ \mapsto\ Q(2, 2)\\ \\ \mapsto\ R(-3, -3)\end{gathered}

↦ P(1,1)

↦ Q(2,2)

↦ R(−3,−3)

Hence, the coordinates of the centroid will be,

\large\text{$\left(\dfrac{1+2-3}{3},\ \dfrac{1+2-3}{3}\right

)\ \ \ \ \ \Longrightarrow\ \ \ \ \ $}\Large\text{$\bold{\left(0,\ 0\right)}$}(

3

1+2−3

,

3

1+2−3

) ⟹ (0, 0)

Hence, origin is the centroid!

Hope it helped

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