Question

Calculate the length of PG where G the centroid is.

15. The vertices of a triangle are P (−4,2), Q (0,6), and R(7, −2) as shown on the following grid

Answer 1

To find the centroid, we take the average of the x-coordinates and the average of the y-coordinates of the three vertices.

Average of x-coordinates:
(-4 + 0 + 7)/3 = 1

Average of y-coordinates:
(2 + 6 - 2)/3 = 2

Therefore, the centroid G is at point (1,2).

To find the length of PG, we use the distance formula:

PG = sqrt((1-(-4))^2 + (2-2)^2)

PG = sqrt(5^2 + 0^2)

PG = sqrt(25)

PG = 5

Therefore, the length of PG is 5 units.