Answer:
Part a) [tex]G.F=13\ units[/tex]
Part b) [tex]A.F=39\ units[/tex]
Part c) [tex]F.C=22\ units[/tex]
Part d) [tex]G.B=24\ units[/tex]
Part e) [tex]D.B=36\ units[/tex]
Step-by-step explanation:
we know that
The centroid of a triangle is the point where the three median.s coincide.
The centroid is located two thirds of the distance from any vertex of the triangle.
step 1
Find the value of A.F.
we know that
[tex]A.G=\frac{2}{3} A.F[/tex]
we have
[tex]A.G=26\ units[/tex]
substitute
[tex]26=\frac{2}{3} A.F[/tex]
Solve for A.F.
[tex]A.F=26(3)/2[/tex]
[tex]A.F=39\ units[/tex]
step 2
Find the value of G.F.
[tex]G.F=\frac{1}{3} A.F[/tex]
substitute the value of A.F
[tex]G.F=\frac{1}{3} (39)=13\ units[/tex]
step 3
Find the value of F.C.
Remember that a median of a triangle is a line segment from one vertex to the mid-point on the opposite side of the triangle
so
[tex]F.C=\frac{1}{2}B.C[/tex]
we have
[tex]B.C=44\ units[/tex]
substitute
[tex]F.C=\frac{1}{2}(44)[/tex]
[tex]F.C=22\ units[/tex]
step 4
Find the value of D.B.
[tex]D.G=\frac{1}{3} D.B[/tex]
we have
[tex]D.G=12\ units[/tex]
substitute
[tex]12=\frac{1}{3} D.B[/tex]
[tex]D.B=12(3)=36\ units[/tex]
step 5
Find the value of G.B
[tex]G.B=\frac{2}{3} D.B[/tex]
substitute the value of D.B.
[tex]G.B=\frac{2}{3} (36)[/tex]
[tex]G.B=24\ units[/tex]
