In triangle PQR, \(P(-4,\,3)\) and \(Q(6,\,-1)\), and the medians of the triangle meet at \(G(1,\,2)\). What are the coordinates of R?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \((1,\,4)\)
The medians meet at the centroid G, whose coordinates are the averages of the coordinates of the three vertices. So the sum of the three x-coordinates is 3 times the x-coordinate of G, and the same for y.
Let \(R=(x,\,y)\)
\(-4+6+x=3\times1=3\), so \(x=1\)
\(3+(-1)+y=3\times2=6\), so \(y=4\)
So \(R=(1,\,4)\)
Check: \(\displaystyle \left(\frac{-4+6+1}{3},\,\frac{3-1+4}{3}\right)=(1,\,2)=G\)
