Question

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

Answer 1

Line eq joining A and B

Y +6= 2/-6 ( x-5)

Y +6 = -1/3( x-5)

Take intersection of y axis with this line

X=0

Y+ 6 = 5/3

Y= -13/3

Coordinate = 0,-13/3)

Answer 2

Given points are A(5,-6) and B(-1,-4).

Here (x1,y1) = (5,-6), (x2,y2) = (-1,-4), (m,n) = (k,1)

Let the y-axis divides the line segment in the ratio k:1 and point of intersection be (0,y).

We know that coordinates of points dividing the line segment joining (x,1,y1) and (x2,y2) in the ratio m:n is

⇒ [(mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)]

$=>[\frac{k(-1) + 1(5)}{k + 1}, \frac{k(-4) + 1(-6)}{k + 1}]$

Given that the point lies on y-axis.So, its x-coordinate is 0.

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

$= > k(-1) + 1(5) = 0$

$= > -k + 5 = 0$

$= > k = 5$

Hence, the required ratio is 5:1.

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Now,

Substitute k = 5, we get the coordinates.

$= > [\frac{5(-1) + 1(5)}{5 + 1}, \frac{5(-4) + 1(-6)}{5 + 1}]$

$= > [\frac{0}{6}, \frac{-20 - 6}{6}]$

$= > [0, \frac{-26}{6}]$

$= > [0, \frac{-13}{3}]$

Therefore, the coordinates of the point of division is (0, -13/3).

Hope this helps!