The centroid of the region shown in the figure below enclosed by the graphs of , , and lies on:
A) the line
B) the line
C) the line
D) the graph of
E) the graph of

Question

The centroid of the region shown in the figure below enclosed by the graphs of  ,  , and  lies on: 
A) the line 
B) the line 
C) the line 
D) the graph of 
E) the graph of

Quizplus · Accepted Answer

The centroid of a region lies at the intersection of medians. 
The equation of the line passing through the midpoint of the line segment joining the points (0,3) and (3,0) and the point (2,2) is y=x. 
Similarly, the equation of the line passing through the midpoint of the line segment joining the points (0,3) and (3,6) and the point (2,2) is y=2x-1. 
Now, the equation of the median passing through the point (2,2) and parallel to the x-axis is y=2. 
The intersection of this line with the median passing through the point (2,2) and parallel to y-axis, which is x=2, gives us the centroid at point (2,2). 
Therefore, the centroid lies on the line x=2, which is Choice C.

The Centroid of the Region Shown in the Figure Below