Point G is the centroid of the right △ABC with hypotenuse AB=18 in. Find CG.
2 answers:
Answer:
CG = 6 in.
Step-by-step explanation:
Given information : Point G is the centroid of the right △ABC with hypotenuse AB=18 in.
We know that circumcenter of a right angle triangle is the midpoint of the hypotenuse.
Let point M be the circumcenter of △ABC.
Hypotenuse AB=18 in.
Radius of circumcircle = in.
Know connect the circumcenter M with the vertex C. CM is a median of the △ABC from vertex C.
MC = radius of the circumcircle = 9 in.
We know that centroid divides each median in a ratio of 2:1.
Point G is the centroid of the right △ABC. It means point G divides CM median in a ratio of 2:1.
Therefore, the measure of CG is 6 in.
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Answer:
The coordinate of point M = (-6,7)
Explanation:
The Median of a triangle is a line segment from a vertex to the midpoint of the opposite side of a triangle.
Given: has vertices T(3,6) , R(-3,10) and E(-9,4).
Here, line TM is a median of triangle TRE where M is the midpoint of RE.
The midpoint of M of the line segment from R(-3,10) to E(-9,4) is;
M =
Therefore, the coordinate of point M is, (-6,7).