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प्रश्न
Points P and Q trisect the line segment joining the points A(−2, 0) and B(0, 8) such that P is near to A. Find the coordinates of points P and Q.
उत्तर
P and Q trisect line joining the points A and B.
Let the coordinates of P and Q be (a, b) and (c, d) respectively.
P is the midpoint of AQ.
`(-2 +"c")/2 = "a" and (0+"d")/2 = "b"`
⇒ c= 2a + 2 and d = 2b ...........(1)
Also, Q is the mid point of PB.
`("a"+0)/2 ="c" and ("b"+8)/2 = "d"`
⇒ `"a"/2 = "c" and ("b"+8)/2 ="d"` .........(2)
From (1) and (2) we have
2a + 2 =`"a"/2`
⇒ 4a + 4 = a
⇒ 3a = -4
⇒`"a" = -4/3`
Also,
2b `=("b"+8)/2`
⇒ 4b = b +8
⇒ b = `8/3`
Putting these values of a and b in (2)
`((-4)/3)/2 = "c"`
⇒ `(-2)/3 = "c"`
And
`(8/3+8)/2 = "d"`
`((8+24)/3)/2 = "d"`
⇒`(32/2)/2 = "d"`
⇒ `16/3 = "d"`
Thus, the points are P `((-4)/3 , 8/3)` and Q `((-2)/3 , 16/3).`
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