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.
Answers
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 :-
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'
Equating the both 'x - co-ordinates ' :-
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) = (0/6 , -26/6)
(0 , y) = (0 , -13/3)
∴ Point of intersection = (0 , y) = (0 , -13/3)