00:02
We are given a region and we are asked to find the centroid of this region by locating the centroids of the rectangles and triangles in the region and to use addativity of moments.
00:15
This is in reference to exercise 40 of this section.
00:19
We see that the region is composed of a rectangle in the second quadrant with vertices negative 1 -0 -0 -0 -2 and negative -1.
00:34
A triangle in the first quadrant with vertices 0 ,0, and 02.
00:46
Well, we have that the rectangle to the left of the y -axis has a centroid, which is the average of the x values, negative 1 half, and the average of the y values, 1.
01:10
This is the center of the rectangle, and has an area which is 1 times 2 or 2.
01:27
Likewise, we have that the triangle to the right of the y -axis has an area which is 1 half times 2, which is 2, and has a centroid, which by the previous exercise, the centroid is the median of the triangle.
02:08
So it's going to be two -thirds of the way from the vertex zero -zero to the point one -one.
02:21
So the centroid is two -thirds, two -thirds...