Answer: The answer is \(\dfrac{5}{3}.\)
Step-by-step explanation: Given that the co-ordinates of point G and H are (3, -1) and (-2, 3) respectively.
We are to find the y-value of the point P that is located at two-third distance from point G to point H.
As shown in the attached figure, the ration in which the point P divides the line segment GH is 2 : 1.
Therefore, the co-ordinates of point P will be
\(\left(\dfrac{2\times (-2)+1\times 3}{2+1},\dfrac{2\times 3+1\times (-1)}{2+1}\right)\\\\\\=\left(\dfrac{-4+3}{3},\dfrac{6-1}{3}\right)\\\\=\left(\dfrac{-1}{3},\dfrac{5}{3}\right).\)
Thus, the y-value of the point P is \(\dfrac{5}{3}.\)
