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Question 5: Given the directed line segment MP with M(-12,-5) and P(9, -12), if N lieson MP such that the ratio of MN to NP is 3:4, find the coordinates of N.

Answer :

M(-12, 5)

P(9, -12)

Let:

N (xp, yp )

ratio a:b

xp = x1 + a/(a+b) (x2-x1)

yp = y1 + a/(a+b) (y2-y1)

Where:

x1 = -12

x2 = 9

y1 = -5

y2 = -12

a = 3

b= 4

Replacing the values:

xp = -12 + 3/(3+4) (9- (-12)) = -12 + 3/7 (21) = -3

yp = -5 + 3/(3+4) (-12 - (-5)) = -5 + 3/7 (-7) = -8

The coordinates of N are:

N = (-3,-8 )

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