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The $Y$ -axis divide the line segment joining the points $P (− 4, 5)$ -axis divide the line segment joining the pointsand $Q (3, − 7)$ andin the ratio ____.

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Detailed Solution

The

Y

-axis divide the line segment joining the points

P (− 4, 5)

and

Q (3, − 7)

in the ratio 4:3.
We have been given two points

P (− 4, 5)

and

Q (3, − 7)

.
Using the section formula

(x, y) ≡ m x 2 + n x 1 m + n, m y 2 + n y 1 m + n

.
We know the required point lies on the y-axis.
Thus, its x-coordinate must be zero.
So, the coordinates of the required point be (0,y).
Let the required ratio be m:n, and

x_{1} = - 4, x_{2} = 3

.
Substituting the values,

0 = m (3) + n (− 4) m + n ⇒ 3 m − 4 n = 0 ⇒ m n = 43

Therefore, the required ratio is 4:3.

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