Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form
line segments A E, B F, and C D. The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6.
G is the centroid of triangle ABC.
What is the length of AE?
units
G is the centroid of triangle ABC.
What is the length of AE?
units
2 answers:
Answer:
28/3
Step-by-step explanation:
A median of a triangle is a segment from a vertex to the midpoint of the opposite side. The three medians of a triangle are concurrent. The point of concurrency, called the centroid, is inside the triangle and The centroid of a triangle is two-thirds of the distance from each vertex to the midpoint of the opposite side.
AG = 2x+10
FG = 2x -1
GB= 3x + 6
As we already knew in the principle, so GB= 2FG
<=> 3x + 6 = 2( 2x -1)
<=> 4x= 8
<=> x =2
So, AG = 2*2+10 =14
But AG = 2/3AE, so AE = 2/3*14 = 28/3
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Answer:
-3
Step-by-step explanation:
The line passes through (1,0) and (0,3)
Slope = Change in y ÷ change in x
Slope = = -3