Answer:
Part a) [tex]ML=15\ units[/tex]
Part b) [tex]HM=30\ units[/tex]
Part c) [tex]JM=21\ units[/tex]
Part d) [tex]MI=42\ units[/tex]
Part e) [tex]GM=40\ units[/tex]
Part f) [tex]MK=20\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.
The centroid is located two thirds of the distance from any vertex of the triangle
Part a) Find ML
we have
[tex]HL=45\ units[/tex]
we know that
[tex]ML=\frac{1}{3}HL[/tex]
substitute the given value
[tex]ML=\frac{1}{3}(45)[/tex]
[tex]ML=15\ units[/tex]
Part b) Find HM
we have
[tex]HL=45\ units[/tex]
we know that
[tex]HM=\frac{2}{3}HL[/tex]
substitute the given value
[tex]HM=\frac{2}{3}(45)[/tex]
[tex]HM=30\ units[/tex]
Part c) Find JM
we have
[tex]JI=63\ units[/tex]
we know that
[tex]JM=\frac{1}{3}JI[/tex]
substitute the given value
[tex]JM=\frac{1}{3}(63)[/tex]
[tex]JM=21\ units[/tex]
Part d) Find MI
we have
[tex]JI=63\ units[/tex]
we know that
[tex]MI=\frac{2}{3}JI[/tex]
substitute the given value
[tex]MI=\frac{2}{3}(63)[/tex]
[tex]MI=42\ units[/tex]
Part e) Find GM
we have
[tex]KG=60\ units[/tex]
we know that
[tex]GM=\frac{2}{3}KG[/tex]
substitute the given value
[tex]GM=\frac{2}{3}(60)[/tex]
[tex]GM=40\ units[/tex]
Part f) Find MK
we have
[tex]KG=60\ units[/tex]
we know that
[tex]MK=\frac{1}{3}KG[/tex]
substitute the given value
[tex]MK=\frac{1}{3}(60)[/tex]
[tex]MK=20\ units[/tex]
