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OAB is a triangle
OA = 4a and OB = 5b
M is the midpoint of OB
AN:NB = 2:3
Find OP:PN

OAB is a triangle OA 4a and OB 5b M is the midpoint of OB ANNB 23 Find OPPN class=

Respuesta :

Answer:

5:2

Step-by-step explanation:

ON = OA + AN

AN = 2/5AB

AB = 5b-4a

AN = 2b - 8/5a

ON = 4a - 8/5a +2b

ON = 12/5a+2b

OP = k(12/5a+2b)

OP = OA + AP

AP = x(AM)

AM = 5/2b-4a

OP=4a-4ax+5/2bx

OP=4a-4ax+5/2bx and OP=12/5ak+2bk

Coefficients of A

4-4x=12/5k

k=(20-20x)/12

Coefficients of B

5/2x=2k

k=5/4x

(20-20x)/12 =5/4x

20=35x

x=4/7

k=5/4 * 4/7 = 5/7

OP=k(ON)

OP = 5/7

PN = 2/7

OP:PN = 5:2

I figured it out after posting the question, typing from a different account. I hope this helps somebody.