Question

Find the centroid of the triangle with these vertices: P (-1,7), Q (9,5), and R (4,3).

Answer 1

Answer:

The coordinates of the centroid are:

$O\:=\:\left(4,\:5\right)\:\:$

The diagram is also attached below.

Step-by-step explanation:

Given the vertices

• P (-1, 7)

• Q (9, 5)

• R (4, 3)

We know that the intersection of medians brings the centroid of the triangle.

The centroid of a triangle is given by

$O\:=\:\left(\frac{P_x+Q_x+R_x}{3},\:\frac{P_y+Q_y+R_y}{3}\:\right)$

In this example,

$P_x=-1,\:P_y=7$

$Qx=9,\:Q_y=5$

$Rx=4,\:R_y=3$

substituting in the formula

$O\:=\:\left(\frac{-1+9+4}{3},\:\frac{7+5+3}{3}\:\right)\:\:$

$O\:=\:\left(\frac{12}{3},\:\frac{15}{3}\:\right)\:\:$

$O\:=\:\left(4,\:5\right)\:\:$

Therefore, the coordinates of the centroid are:

$O\:=\:\left(4,\:5\right)\:\:$

The diagram is also attached below.