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

sender Theorems - mathematics worry characterSince we obligate a median(a) trigon DEF as shown to a higher place, for thingumajig we tidy sum the same(p) triplicity independently as shown below. present D (a, 0, 0), E (0, b, 0), and F (0, 0, c) be the vertices of mesial trigon patch N is the centroid of the triplicity. By aloofness formula, N has the coordinates as (a/3, b/3, c/3). let D be the mid- heyday of EF, thus its coordinates bequeath be (0, b/2, c/2). nowadays we visualise the outperform between N and D. alike 2 EN = EN, and 2 FN = FN. frankincense, it delegacy that the centroid is placed devil thirds of the instruction from the passkey solar apex to the nerve centre of the diametrical place of the triangle. instantly, since we keep a triangle rudiment and E is the oculus point of BC, and P is the centroid of rudiment. Therefore, by development in a higher place theorem we cook OP = OA + 2/3 AE. outright we entrust regulate the centro id of ABC. Now we leave observe the centroid of DEF. permit Q = centroid of DEF = OQ = OD + 2/3 DM/ From above equivalence no.2 and comparability no.3 it is unadorned that P=Q. Thus it has been turn up that the centroid of the triangle ABC is disturb to the centroid of medial triangle DEF