Answer: The required co-ordinates of he point K are (9.2, 7).
Step-by-step explanation: Given that the the endpoint of MP are M(2,1) and P(14,10) and the point K partitions MP in the ratio of MK : KP = 3 : 2.
We are to find the co-ordinates of point K.
We know that
the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).[/tex]
For the given division, m : n = 3 : 2.
Therefore, the co-ordinates of the point K are
[tex]\left(\dfrac{3\times14+2\times2}{3+2},\dfrac{3\times10+2\times1}{3+2}\right)\\\\\\=\left(\dfrac{42+4}{5},\dfrac{30+2}{5}\right)\\\\=\left(\dfrac{46}{5},\dfrac{35}{5}\right)\\\\=(9.2,7).[/tex]
Thus, the required co-ordinates of the point K are (9.2, 7).
