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
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.