Question

find the ratio in which y axis divides the line segment joining the points a(3,2) b(-1,2)​

Answer 1

Answer:

Given:

Find the ratio in which y axis divides the line segment joining the points a(3,2) b(-1,2).

Let us assume L:1 be line dividing into ratio:

1. x - co-coordinates,
2. y - co-coordinates.

=> my2 + ny1 / m + n

=> mx2 + nx1 / m + 2

Adding values we get , x-axis:

=> 3 + L / L + 1 = 0

=> L = | - 3 | = 3

=> 3 : 1 is ratio:

Answer 2

Answer:

y-axis divide the line in the ratio 1:3.

Given:

y axis divides the line segment joining the points a(3,2) b(-1,2)​

To find:

find the ratio

Step-by-step explanation:

When line divides the line segment joining points $(x_{1}, y_{1}) , (x_{2}, y_{2})$ in the ratio m:n then, we know that the coordinates of points are given by,

$\frac{(mx_{2} +nx_{1} ) }{m+n} , \frac{(my_{2} +ny_{1}) }{m+n}$

Let us consider the ratio in which the y-axis divide line segment is m:n.

so, coordinates of point will be,

$\frac{(mx_{2} +nx_{1} ) }{m+n} , \frac{(my_{2} +ny_{1}) }{m+n}\\\frac{(3m - n)}{m+n} , \frac{(2m + 2n)}{m+n}$

as point lies on y-axis its coordinates will be

(0,y)

So,

equate the x-coordinate with 0

i.e.

$\frac{(3m - n)}{m+n} = 0\\3m - n = 0\\3m = n\\m = \frac{n}{3}\\ \frac{m}{n} = \frac{1}{3}$

Hence, the y-axis divide the line in the ratio 1:3.

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