Question

The endpoint of MP are M(2,1) and P(14,10). If point K partitions MP in aratio of MK:KP=3:2, what are the coordinates of K?

Answer 1

2(2,1)(14,10)

(4,2) - (14,10)= (-10, -8)

The coordinates of K are (-10, -8).

Answer 2

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

`\left((mc+na)/(m+n),(md+nb)/(2)\right).`

For the given division, m : n = 3 : 2.

Therefore, the co-ordinates of the point K are

`\left((3*14+2*2)/(3+2),(3*10+2*1)/(3+2)\right)\\\\\\=\left((42+4)/(5),(30+2)/(5)\right)\\\\=\left((46)/(5),(35)/(5)\right)\\\\=(9.2,7).`

Thus, the required co-ordinates of the point K are (9.2, 7).