Vector Theorems Math Problem Example | Topics and Well Written Essays - 500 words

Vector Theorems - Math Problem Example Since we have a medial triangle DEF as shown above, for convenience we draw the same triangle separately as shown below. Here D (a, 0, 0), E (0, b, 0), and F (0, 0, c) be the vertices of medial triangle while N is the centroid of the triangle. By distance formula, N has the coordinates as (a/3, b/3, c/3). Let D†² be the mid-point of EF, therefore its coordinates will be (0, b/2, c/2). Now we find the distance between N and D†². Similarly 2 E†²N = EN, and 2 F†²N = FN. Thus, it means that the centroid is located two thirds of the way from the original vertex to the midpoint of the opposite side of the triangle. Now, since we have a triangle ABC and E is the middle point of BC, and P is the centroid of ABC. Therefore, by using above theorem we have OP = OA + 2/3 AE. Now we will find the centroid of ABC. Now we will find the centroid of DEF. Let Q = centroid of DEF = OQ = OD + 2/3 DM/ From above equation no.2 and equation no.3 it is evident that P=Q. Thus it has been proved that the centroid of the triangle ABC is equal to the centroid of medial triangle DEF