Question

o find the ratio in which the line segment
joining the points A(3,8) and B (-9, 3) is
divided by the y axis.​

Answer 1

Answer:

Hey!

Pls refer to the attatched image for answer

Answer 2

Answer :-

The ratio in which the line segment  joining the points A(3,8) and B (-9, 3) is  divided by the y axis is 1 : 3.

Solution :-

Let the required ratio be k : 1.

Here,

$x_1 = 3,\:\:\:\:y_1 = 8,\:\:\:\:m_1 = k,\\x_2 = -9,\:\:\:\:y_2 = 3,\:\:\:\:m_2 = 1$

We will use section formula to find the ratio.

Section formula -

=> (x, y) = $\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\dfrac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}$

=> (x, y) = $\dfrac{k\times -9+1\times 3}{k+1},\dfrac{k\times 3+1\times 8}{k+1}$

=> (x, y) = $\dfrac{-9k+3}{k+1},\dfrac{3k+8}{k+1}$

But this is a point on the y- axis, so

=> $\dfrac{-9k+3}{k+1} = 0$

=> $-9k+3 = 0\times (k+1)$

=> $-9k+3 = 0$

=> $-9k = -3$

=> $k = \dfrac{-3}{-9}$

=> $k = \dfrac{1}{3}$

The ratio is

=> k : 1

=> $\dfrac{1}{3} : 1$

=>  ${\dfrac{\dfrac{1}{3}}{1}}$

=>  $\dfrac{1}{3}$

=> 1 : 3