Question

The line segment joining the points A(3, –4) and B(1, 2) is
trisected at the points P and Q such that P is nearer to A. If the
co-ordinates of P and Q are (p, – 2) and (5/3, q) respectively, find
the values of p and q.

Answer 1

Answer:

p = 7/3 and q = 0

Step-by-step explanation:

The trisection points are given by the weighted averages:

P = ( 2A + B ) / 3

  = (  (2×3 + 1) / 3,  (2×-4 + 2) / 3  )

  = ( 7/3, -6/3 )

  = ( 7/3, -2 )            [ good news... the y coordinate given in the question is correct! ]

and

Q = ( A + 2B ) / 3

   = (  (3 + 2×1) / 3,  (-4 + 2×2) / 3  )

   = ( 5/3, 0/3 )

   = ( 5/3, 0 ).         [ good news... the x coordinate given in the question is correct! ]

From the above, we have

p = 7/3 and q = 0

Answer 2

The trisection points are given by the weighted averages:

P = ( 2A + B ) / 3

  = (  (2×3 + 1) / 3,  (2×-4 + 2) / 3  )

  = ( 7/3, -6/3 )

  = ( 7/3, -2 )            [ good news... the y coordinate given in the question is correct! ]

and

Q = ( A + 2B ) / 3

   = (  (3 + 2×1) / 3,  (-4 + 2×2) / 3  )

   = ( 5/3, 0/3 )

   = ( 5/3, 0 ).         [ good news... the x coordinate given in the question is correct! ]

From the above, we have

p = 7/3 and q = 0

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