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The line segment joining the points A(3,...

The line segment joining the points A(3, -4) and B(1, 2) is trisected at the points P(p, -2) and `Q((5)/(3), q)`. Find the values of p and q.

Text Solution

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The correct Answer is:
`p = (7)/(3), q = 0`
P divides AB in the ratio 1:2.
This point is `P((1 xx 1 + 2 xx 3)/(1+2), (1 xx 2 + 2 xx (-4))/(1+2))`.
`therefore ((7)/(3), -2) -=(p, -2) rArr p = (7)/(3)`.
Q divides AB in the ratio 2:1. So, we get
`Q((2 xx 1 + 1 xx 3)/(2+1), (2 xx 2 + 1 xx (-4))/(2+1)), i.e., ((5)/(3), 0)`
`therefore ((5)/(3), 0) -=((5)/(3), q) rArr q = 0`.
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