Question

find the ratio in which the line segment joining the points A(a1,b1) and B(A2, b2) is divided bz Y axis​

Answer 1

Given : line segment joining the points A(a1,b1) and B(A2, b2) is divided by Y axis​

To Find : ratio

Solution:

At Y axis  x coordinate is 0

A(a₁,b₁) and B(a₂, b₂)

Let say Y axis divided points A & B in k : 1  Ratio

=> 0  =  (ka₂ + a₁)/(k + 1)

=> 0 = ka₂ + a₁

=>  ka₂  = -a₁

=> k =  -a₁/a₂

=> k : 1 =   -a₁  : a₂

ratio in which the line segment joining the points A(a1,b1) and B(A2, b2) is divided bz Y axis​  is -a₁  : a₂

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Answer 2

Answer:

The ratio is -a1 : a2

Step-by-step explanation:

Given : Two points ( a1, b1 ) and ( a2, b2) .

To Find : Ratio in which line joining given point is divided by y axis.

Line joining is divided by y axis

Let the point on y axis be ( 0 , y)

Also, let the ratio be k : 1

Now we can use Section Formula, Co-ordinate of point in ratio m : n is given by

( ma2 + ma1 / m + n, mb2 + nb1 / m + n)

Now using this formula we get

( 0 , y) = ( ka2 + 1 × a1 / k + 1 , kb2 + 1 × b1 / k + 1 )

0 = ka2 + a1 / k + 1

ka2 + a1 = 0

ka2 = -a1

k = -a1 / a2

k : 1 = -a1 / a2 : 1

k : 1 = -a1 : a2