Question

1. graph and give the coordinates of the centroid of △rst. circumcenter: ( , )

Explanation:

Step1: Assume coordinates

Let's assume the coordinates of \(R(x_1,y_1)\), \(S(x_2,y_2)\) and \(T(x_3,y_3)\) from the graph. Suppose \(R(- 3,5)\), \(S(3,5)\) and \(T(0, - 1)\).

Step2: Use centroid formula

The formula for the centroid of a triangle with vertices \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\) is \(G(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})\).
Substitute \(x_1=-3\), \(x_2 = 3\), \(x_3=0\), \(y_1 = 5\), \(y_2=5\) and \(y_3=-1\) into the formula.
For the \(x\) - coordinate of the centroid: \(\frac{-3 + 3+0}{3}=0\).
For the \(y\) - coordinate of the centroid: \(\frac{5 + 5-1}{3}=\frac{9}{3}=3\).

Answer:

\((0,3)\)