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Question
Show that the line segment joining the points (-3, 10) and (6, -5) is trisected by the coordinates axis.
Solution
Let the coordinates of two points x-axis and y-axis be P (x, O) and G (0, y) respectively.
Let P divides AB in the ratio k : 1.
Coordinates of P are
P (x , 0) = P `((6"k" - 3)/("k" + 1) , (- 5 "k" + 10)/("k" + 1))`
⇒ 0 = `(- 5 "k" + 10)/("k" + 1)`
⇒ 5 k = 10
⇒ k = 2
Hence P divides AB in the ratio 2: 1.
Let Q divides AB in the ratio k1 : 1.
Coordinates of Q are,
Q (0 , y) = Q `((6"k"_1 - 3)/("k" + 1) , (-5"k" + 10)/("k" + 1))`
`=> 0 = (6"k"_1 - 3)/("k" + 1)`
⇒ 6k1 = 3
⇒ `"k"_1 = 1/2`
Hence Q divides AB in the ratio 1: 2
Hence proved, P and Q are the points of trisection.
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