Question

FIND THE RATIO IN WHICH THE LINE SEGMENT JOINING THE POINT A[3;8] AND B [-9 ;3 ]IS DIVIDED BY Y AXIS

Answer 1

Answer:

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Answer 2

Answer:

1 : 3

Step-by-step explanation:

Given ,

A = (3 , 8)

B = (-9 , 3)

A , B are divided by y-axis

To Find :-

Ratio that y- axis divides 'A' and 'B'

How To Do :-

As they said that 'A , B' is divided by y-axis we need to find the co-ordinate of 'y-axis and we need to equate that co-ordinates to section (Internal division) formula after we need to equate both 'x terms and 'y' terms . We can see that If we equate the both 'x' terms first then we can get the value of the ratio because if we equated the both 'y' terms there will be a variable so we can not get the value.

Formula Required :-

Section(Internal Division) Formula :-

$=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Solution :-

Co-ordinates of 'y' co-ordinate :-

= (0 , y)

A = (3 , 8)

Let ,

x_1 = 3 , y_1 = 8

B = (-9 , 3)

Let ,

x_2 = - 9 , y_2 = 3

Let the ratio be 'm : n'

Substituting in the formula :-

$(0,y)=\left(\dfrac{m(-9)+n(3)}{m+n},\dfrac{m(3)+n(8)}{m+n}\right)$

$(0,y)=\left(\dfrac{-9m+3n}{m+n},\dfrac{3m+8n}{m+n}\right)$

Equating both 'x' terms and 'y' terms :-

$0=\dfrac{-9m+3n}{m+n},y=\dfrac{3m+8n}{m+n}$

Equating 'x' terms first :-

$0=\dfrac{-9m+3n}{m+n}$

0 (m + n) = -9m + 3n

0 = - 9m + 3n

9m = 3n

9m/n = 3

m/n = 3/9

m/n = 1/3

m : n = 1 : 3

∴ The ratio that y-axis divides 'A and B' is :- ' 1 : 3'