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Elden [556K]
3 years ago
5

Points A, P and B are collinear such that P sits on line segment AB and partitions the segment so that AP to PB is in the ratio

2:3. Point A is located at (3,-1) and B is located at (8,14). Find the coordinates of P, the partition point.
Mathematics
1 answer:
arlik [135]3 years ago
8 0

Answer:

  P = (5, 5)

Step-by-step explanation:

For the given division, ...

  P = (2B +3A)/5

  P = (2(8, 14) +3(3, -1))/5 = (16+9, 28-3)/5 = (25, 25)/5

  P = (5, 5)

_____

For some division ratio of AP : PB = p : q, we have ...

  (P -A)/(B -P) = p/q

  q(P -A) = p(B -P)

  P(p+q) = pB +qA . . . . rearranging

  P = (pB +qA)/(p+q) . . . . . the formula we used above

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This would be a big help so plzzz help me =/
nikdorinn [45]

The correct order would be:

5/64 x 3, 1/16 x 3, 3/32 x 4, 11/64 x 4, 7/16 x 3, 3/4 x 2, 3/8 x 4, 1 7/8 x 4, 2.25 x 2, 1.5 x 4, 3 3/8 x 3, 3.75 x 3

First we have to take all of the numbers and do the multiplication. It's often easiest to turn them in to decimals so that you have a common form.

3/32 x 4 = 3/8 = .375

3/4 x 2 = 3/2 = 1.5

1 7/8 x 4 = 15/4 = 3.75

2.25 x 2 = 4.5

1.5 x 4 = 6

3/8 x 4 = 3/2 = 1.5

5/64 x 3 = 5/32 = .156

3.75 x 3 = 11.25

1/16 x 3 = 3/16 = .1875

7/16 x 3 = 21/16 = 1.31

3 3/8 x 3 = 81/8 = 10.125

11/64 x 4 = 11/16 = .687

Now we can use those to put in order.

5/64 x 3 = 5/32 = .156

1/16 x 3 = 3/16 = .1875

3/32 x 4 = 3/8 = .375

11/64 x 4 = 11/16 = .687

7/16 x 3 = 21/16 = 1.31

3/4 x 2 = 3/2 = 1.5

3/8 x 4 = 3/2 = 1.5

1 7/8 x 4 = 15/4 = 3.75

2.25 x 2 = 4.5

1.5 x 4 = 6

3 3/8 x 3 = 81/8 = 10.125

3.75 x 3 = 11.25

Which if you are looking for without the extra terms, you can check the answer at the top.

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