Question

find the ratio in which the y-axis divides the line segment of point of (-1,-4) and (5,-6) . also find the coordinate of point of intesection

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 coordinates of point of intersection are $(0,-\frac{-13}{3})$.

Step-by-step explanation:

Let y-axis divides the line segment of point of (-1,-4) and (5,-6) in k:1.

The x-coordinate of point of intersection is 0.

Section formula:

If a point divides a line segment in m:n whose end points are $(x_1,y_1)$ and $(x_2,y_2)$, then the coordinates of that point are

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

Using section formula the x-coordinate of point of intersection is

$x-coordinate=\frac{k(5)+1(-1)}{k+1}$

$0=\frac{5k-1}{k+1}$

$0=5k-1$

$1=5k$

$\dfrac{1}{5}=k$

$k:1=\dfrac{1}{5}:1=1:5$

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

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

$y-coordinate=\frac{-26}{6}$

$y-coordinate=-\frac{-13}{3}$

Therefore, the coordinates of point of intersection are $(0,-\frac{-13}{3})$.

#Learn more

Find the coordinator of point p if p divdes the lines segment joining the point A ( -2,8) and (5,-4) in the ratio 2:3.

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