Answer: The required y co-ordinate of P is 2.2.
Step-by-step explanation: Given that the points J(-2,1) and K(4,5) form line segment JK and a point P partitions JK in the ratio 3: 7.
We are to find the y co-ordinate of P.
We know that
the co-ordinates of a point that divides the line segment with endpoints (a, b) and (c, d) are given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
For the given partition, we have
(a, b) = (-2, 1), (c, d) = (4, 5) and m : n = 3 : 7.
Therefore, the y co-ordinates of point P is
[tex]\dfrac{md+nb}{m+n}=\dfrac{3\times5+7\times1}{3+7}=\dfrac{22}{10}=2.2.[/tex]
Thus, the required y co-ordinate of P is 2.2.
