Question

find the ratio in which the y axis divides the line segment joining the points (5,-6) and (-1,-4). Also find the coordinates of the point of division.

Answer 1

let the coordinates of the point be (0,y) and the y axis divide the line segment in the ratio k:1

(0,y)={(-k+5)/k+1 , (-4k-6)/k+1}

=>0=-k+5/k+1

=>0=-k+5

=>k=5

y=-4k-6/k+1

=>y=-4(5)-6/5+1

=>y=-20-6/6

=>y=-26/6

thus the coordinates of the point is (0,-26/6)

Answer 2

The ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4) is 5: 1.

Step-by-step explanation:

We are given that the y-axis divides the line segment joining the points (5,-6) and (-1,-4).

Let the coordinate on the y-axis which divides the line segment joining the points (5,-6) and (-1,-4) be '(0, y)'.

And also, let the ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4) be 'k: 1'.

As we know that the section formula states that;

$x=\frac{m_1x_2+m_2x_1}{m_1+m_2}$

Since the x coordinate on the y-axis is 0, that means;

$0=\frac{m_1x_2+m_2x_1}{m_1+m_2}$

Here, $x_1 = 5, x_2=-1, m_1 = k \text{ and } m_2= 1$

So,  $0=\frac{(k \times -1)+(1 \times 5)}{k+1}$

$(k \times -1)+(1 \times 5)}=0$

$-k+5=0$

So, k = 5

This means that the ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4) is 5: 1.

Now, to find the coordinates of the point of division, i.e. y coordinate;

$y=\frac{m_1y_2+m_2y_1}{m_1+m_2}$

$y=\frac{(5 \times -4)+(1 \times -6)}{5+1}$

$y=\frac{-20-6}{6}$

$y=\frac{-26}{6}= \frac{-13}{3}$

So, the coordinate of the point of division is $(0, \frac{-13}{3})$.