Question

Find the ratio in which the y axis divide the line segment joining
points A (5,-6) and B (-1,-4). Also find the point of intersection.​

Answer 1

Answer:

1) Ratio = 5 : 1

2)  Point of intersection = (0 , -13/3)

Step-by-step explanation:

Given,

A = (5 , - 6)

B = (-1 , -4)

y-axis divides the line segment AB

To Find :-

1)The ratio that y-axis divides AB.

2)Point of Intersection

How To Do :-

As they given the clue that y-axis we know that the co-ordinates of the y-axis = (0 , y) . So , we need to substitute the value of y-co-ordinates in the section formula . After that we need to equate the both x-co-ordinates to get the value of the ratio 'm : n' . After obtaining the ratio we need to substitute that ratio in the section formula and we need to find the value of 'y'. Here point of intersection means = (0,y) so we need to find the value of 'y' and we need to find the co-ordinates of point of intersection.

Formula Required :-

Section(Internal division) formula :-

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

Solution :-

Co-ordinates of y-axis = (0 , y)

A = (5 , -6)

Let,

x_1 = 5 , y_1 = - 6

B = (-1 , -4)

Let,

x_2 = - 1 , y_2 = - 4

Let , the ratio be 'm : n'

$(0,y)=\left(\dfrac{m(-1)+n(5)}{m+n},\dfrac{m(-4)+n(-6)}{m+n}\right)$

$(0,y)=\left(\dfrac{-m+5n}{m+n},\dfrac{-4m-6n}{m+n}\right)$

Equating the both 'x - co-ordinates ' :-

$0=\dfrac{-m+5n}{m+n}$

0 × (m + n) = -m + 5n

0 = -m + 5n

m = 5n

m/n = 5

→ m : n  = 5 : 1

Ratio = 5 : 1

Substituting the ratio in the above formula to obtain co-ordinates of point of intersection :-

$(0,y)=\left(\dfrac{5(-1)+1(5)}{5+1},\dfrac{5(-4)+1(-6)}{5+1}\right)$

$(0,y)=\left(\dfrac{-5+5}{6},\dfrac{-20-6}{6}\right)$

(0 , y) = (0/6 , -26/6)

(0 , y) = (0 , -13/3)

∴ Point of intersection = (0 , y) = (0 , -13/3)