Question

medians of a triangle practice
complete this assessment to review what youve learned. it will not count toward your grade.
△abc is drawn on a coordinate plane with vertices a(1,3), b(6,6), and c(3,1) and with medians indicating the mid - point of each of the lines ab, bc, and ca. prove that the medians meet at a single point by finding the centroid. express all results in fractions. (1 point)
centroid=( )
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remaining attempts: 3

Explanation:

Step1: Recall centroid formula

The centroid of a triangle with vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$.

Step2: Identify vertex - coordinates

Here, $x_1 = 1,y_1=3,x_2 = 6,y_2 = 6,x_3=3,y_3 = 1$.

Step3: Calculate x - coordinate of centroid

$x=\frac{1 + 6+3}{3}=\frac{10}{3}$.

Step4: Calculate y - coordinate of centroid

$y=\frac{3 + 6+1}{3}=\frac{10}{3}$.

Answer:

$(\frac{10}{3},\frac{10}{3})$