Question

given a line segment AB joining the points A(-4,6)and (8,-3).Find :the ratio in which AB is divided by the yaxis

Answer 1

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Answer 2

The ratio is 1 : 2.

Step-by-step explanation:

The equation of the straight line joining the points A(-4,6) and B(8,-3) will be given by

$\frac{y - (- 3)}{- 3 - 6} = \frac{x - 8}{8 - (- 4)}$

⇒ 12(y + 3) = 9(8 - x)

⇒ 9x + 12y - 36 = 0

Now, the point at which this straight line intersects the y-axis say at P(0,k), then

0 + 12k - 36 = 0

⇒ k = 3

So, the point is P(0,3).

Now, the distance between A(-4,6) and P(0,3) is

$\sqrt{(-4 - 0)^{2} + (6 - 3)^{2}} = 5$ units,

Again, the distance between B(8,-3) and P(0,3) is

$\sqrt{(8 - 0)^{2} + (- 3 - 3)^{2}} = 10$ units.

So, the ratio AP : BP = 5 : 10 = 1 : 2 (Answer)