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

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

$\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).$

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

Therefore, the co-ordinates of the point K are

$\left(\dfrac{3\times14+2\times2}{3+2},\dfrac{3\times10+2\times1}{3+2}\right)\\\\\\=\left(\dfrac{42+4}{5},\dfrac{30+2}{5}\right)\\\\=\left(\dfrac{46}{5},\dfrac{35}{5}\right)\\\\=(9.2,7).$

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

Answer 2

2(2,1)(14,10)

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

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