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Question
In what ratio does the Y-axis divide the line segment P(– 3, 1) and Q(6, 2)?
Solution
Let the line segment PQ be divided by the Y-axis in the ratio k : 1.
Let A be the intersection's point (x, y).
Then, using the section formula,
x = `(mx_2 + nx_1)/(m + n)`
⇒ x = `(6 xx k + (-3) xx 1)/(k + 1)`
⇒ x = `(6k - 3)/(k + 1)`
Now, on Y-axis, x-coordinate = 0
∴ `(6k - 3)/(k + 1)` = 0
⇒ 6k – 3 = 0
⇒ 6k = 3
⇒ k = `3/6 = 1/2`
∴ Ratio = `1/2` : 1 = 1 : 2
As a result, the needed ratio is 1 : 2.
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