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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?

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2(2,1)(14,10)

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

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

User Bopjesvla
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7.6k points
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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).

User Knut Herrmann
by
8.2k points
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