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Alex_Xolod [135]
3 years ago
8

In ABC, and intersect each other at point Q. According to a theorem on medians, Q divides in the ratio 2 : 1. What are the coord

inates of point Q?

Mathematics
1 answer:
Flauer [41]3 years ago
5 0
How to find rapidly the coordinates of Q:
since Q is the center of gravity of the triangle ABC, so we have the following vector relationship
vecQA +vecQB +vecQC =<span>vec0
</span><span>vecQA=(x-3, y+2)
</span><span>vecQB=(x-1, y+5)
</span><span>vecQC=(x-7, y+5)
</span><span>vec0=(0, 0)
</span>
so, vecQA +vecQB +vecQC =<span>vec0 is equivalent to 

</span>x-3 +x-1+x-7 =0, and y+2+y+5+<span>y+5=0 so 3x-11=0 implies x=11/3
</span><span>and 3y+12=0 implies y=-12/3

finally the </span><span>the coordinates of point Q is (11/3, -4)</span><span>

</span>
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