In ΔDEF, the midpoint of the side opposite vertex D is M and the centroid is C. If DM is 33, what are DC and CM?
recall that the centroid is 2/3 of the way between D and M
so whats the answer
22 right?
To find DC and CM in ΔDEF, we can use the properties of a centroid. The centroid divides each median into two segments, with the distance from the centroid to the vertex being two times the distance from the centroid to the midpoint.
Given that DM is 33, we can find DC and CM using this property.
First, we know that CM is twice the distance of the centroid to the midpoint (MC = 2CM). Since M is the midpoint of the side opposite D, CM is also equal to DM/2.
Therefore, CM = DM/2 = 33/2 = 16.5.
Next, DC is twice the distance of the centroid to the vertex (DC = 2CC). This means that DC is equal to twice the length of DM.
Therefore, DC = 2DM = 2 * 33 = 66.
So, the length of DC is 66 and the length of CM is 16.5 in ΔDEF.