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प्रश्न
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
उत्तर
Let P and Q be the points of trisection of the line segment joining A(6, –9) and B(0, 0).
P divides AB in the ratio 1 : 2.
Therefore, the co-ordinates of point P are
`((1 xx 0 + 2 xx 6)/(1 + 2),(1 xx 0 + 2 xx (-9))/(2 + 1))`
=`(12/3, (-18)/3)`
= (4, −6)
Q divides AB in the ratio 2 : 1.
Therefore, the co-ordinates of point Q are
`((2 xx 0 + 1 xx 6)/(2 + 1),(2 xx 0 + 1 xx (-9))/(2 + 1))`
= `(6/3, (-9)/3)`
= (2, –3)
Thus, the required points are (4, −6) and (2, −3).
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