Question

medians of a triangle practice
complete this assessment to review what youve learned. it will not count toward your grade

triangle ( x y z ) is drawn on a coordinate plane with vertices ( x(0,0), y(3,6) ), and ( z(4,3) ) and with medians indicating the midpoint of each line ( x y, y z ), and ( z x ). prove that the medians meet at a single point by finding the centroid. (1 point)
centroid ( =(square, square) )

Explanation:

Step1: Recall the centroid formula

The centroid formula for a triangle with vertices \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\) is \((\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})\)

Step2: Identify the vertices coordinates

Here \(x_1 = 0,y_1=0\), \(x_2 = 3,y_2 = 6\), \(x_3=4,y_3 = 3\)

Step3: Calculate the \(x\)-coordinate of the centroid

\(x=\frac{0 + 3+4}{3}=\frac{7}{3}\)

Step4: Calculate the \(y\)-coordinate of the centroid

\(y=\frac{0 + 6+3}{3}=3\)

Answer:

\((\frac{7}{3},3)\)