The centroid of any triangle is located at the point of intersection of the medians. Recall that a median is a line segment from a vertex to the midpoint of the opposite side. Recall also that the medians intersect at a point two-thirds of the way from each vertex (along the median) to the opposite side. Find the centroid of the region shown, not by integration, but by locating the centroids of the rectangles and triangles (from the above information) and using additivity of moments. (*. F) - ([ y -3 -2 -1 1

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 7E: Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a...
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The centroid of any triangle is located at the point of intersection of the medians. Recall that a median is a line segment from a vertex to the midpoint of the opposite side. Recall
also that the medians intersect at a point two-thirds of the way from each vertex (along the median) to the opposite side.
Find the centroid of the region shown, not by integration, but by locating the centroids of the rectangles and triangles (from the above information) and using additivity of moments.
(*.7) (|
=
y
2
1
-3
-2
1
1
2
-2f
3.
Transcribed Image Text:The centroid of any triangle is located at the point of intersection of the medians. Recall that a median is a line segment from a vertex to the midpoint of the opposite side. Recall also that the medians intersect at a point two-thirds of the way from each vertex (along the median) to the opposite side. Find the centroid of the region shown, not by integration, but by locating the centroids of the rectangles and triangles (from the above information) and using additivity of moments. (*.7) (| = y 2 1 -3 -2 1 1 2 -2f 3.
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