Medians and Centroids
Medians and centroids are fundamental concepts in geometry and statistics, playing crucial roles in various mathematical analyses. In geometry, medians are lines drawn from a vertex of a triangle to the midpoint of the opposite side, while centroids represent the point where these medians intersect. Both medians and centroids offer valuable insights into the geometric properties and balance of shapes. Moreover, in statistics, medians are measures of central tendency, representing the middle value of a dataset when arranged in ascending order, while centroids serve as the geometric center of a distribution. Understanding these concepts is pivotal in both mathematical theory and practical applications.
Questions
- What is the centroid of a triangle with corners at #(2 , 5 )#, #(4 ,7 )#, and #(2 , 7 )#?
- What term describes a line segment that connects a vertex of a triangle to the midpoint of the opposite side ?
- What is the centroid of a triangle with corners at #(4, 7 )#, #(1,2 )#, and #(8 , 5 )#?
- What is the centroid of a triangle with corners at #(5, 1)#, #(4, 9)#, and #(7,2)#?
- What is the centroid of a triangle with corners at #(2 ,1 )#, #(9 ,3 )#, and #(5 , 7 )#?
- What is the centroid of a triangle with corners at #(1 , 1 )#, #(6 , 2 )#, and #(2 , 5 )#?
- Show by construction that the segment that connects the midpoint of two sides of triangle #DeltaABC# is parallel to the third and half it's length?
- What is the centroid of a triangle with corners at #(4,4 )#, #(6,2 )#, and #(2 , 1 )#?
- What is the centroid of a triangle with corners at #(4 , 5 )#, #(3 , 8 )#, and #(7 , 2 )#?
- What is the centroid of a triangle with corners at #(3, 1 )#, #(5, 2 )#, and #(12 , 6 )#?
- What is the centroid of a triangle with corners at #(1 , 3 )#, #(6 , 9 )#, and #(2 , 7 )#?
- What is the centroid of a triangle with corners at #(4,1 )#, #(6,3 )#, and #(5 , 1 )#?
- What is the centroid of a triangle with corners at #(6, 1 )#, #(2, 2 )#, and #(1 , 6 )#?
- What is the centroid of a triangle with corners at #(9 , 5 )#, #(6 , 0 )#, and #(2 , 3 )#?
- In #\triangle DEF#, #M# is the centroid. (i). Find #\overline{MK}# and #\overline{DK}# #" "# (ii). Find #\overline{LM}# and #\overline{LE}# #" "# (iii). Write an expression for #FJ#?
- What is the centroid of a triangle with corners at #(9 , 2 )#, #(4 , 6 )#, and #(5 , 8 )#?
- What is the centroid of a triangle with vertices at #(a, b)#, #(c, d)#, and #(e, f)#?
- What is the centroid of a triangle with corners at #(5, 2 )#, #(2, 5 )#, and #(5,3 )#?
- What is the centroid of a triangle with corners at #(4 , 1 )#, #(3 , 2 )#, and #(5 , 0 )#?
- What is the centroid of a triangle with corners at #(1, 1 )#, #(3, 2 )#, and #(8 , 6 )#?