solve it fast ...
it's urgent ....
Answers
Step-by-step explanation:
Given :-
A straight line passes through P(2,1) and cuts the axes in points A,B and
BP:PA = 3:1
To find :-
1)Find the coordinates of the points A
and B ?
2) Find the equation of the line AB?
Solution :-
Given that :
A straight line passes through P(2,1) and cuts the axes in points A,B and BP:PA = 3:1
From the figure , A lies on the X-axis
Let the Coordinates of A = (x,0)
B lies on the Y-axis
Let the coordinates of B = (0,y)
Given ratio = BP:PA = 3:1
Finding the coordinates of A and B :-
Let (x1,y1) = (x,0) => x1 = x and y1 = 0
Let (x2, y2) = (0,y) => x2 = 0 and y2 = y
Let m1:m2 = 3:1 => m1 = 3 and m2 = 1
We know that
The coordinates of the point which divides the linesegment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 is P(x,y) =
({m1x2+m2x1}/(m1+m2),{m1y2+m2y1}/(m1+m2))
On Substituting these values in the above formula then
=> P(2,1) = ({(3)(0)+(1)(x)}/(3+1),{(3)(y)+(1)(0)}/(3+1))
=> P(2,1) = ({0+x}/4 , {3y+0}/4)
=>P(2,1) = (x/4 ,3y/4)
On Comparing both sides then
=> x/4 = 2 and 3y/4 = 1
=>x = 2×4 and 3y = 1×4
=> x = 8 and 3y = 4
=> x = 8 and y = 4/3
So, Coordinates of A = (x,0) = (8,0)
Coordinates of B = (0,y) = (0,4/3)
Finding the equation of the line AB:-
We have
A = (8,0)
Let (x1, y1) = (8,0) => x1 = 8 and y1 = 0
B = (0,4/3)
Let (x2, y2)=(0,4/3) => x2 = 0 and y2 = 4/3
We know that
The equation of a line passing through the points (x1, y1) and (x2, y2) is
(y-y1)/(x-x1) = (y2-y1)/(x2-x1)
On Substituting these values in the above formula then
=> (y-0)/(x-8) = [(4/3)-0]/(0-8)
=> y/(x-8) = (4/3)/(-8)
=> y/(x-8) = 4/(3×-8)
=> y/(x-8) = 4/-24
=> y/(x-8) = 1/-6
=> y/(x-8) = -1/6
On applying cross multiplication then
=> 6×y = -1(x-8)
=> 6y = -x+8
=> 6y+x-8 = 0
=> x+6y-8 = 0
Answer:-
1) The coordinates of the point A =(8,0)
The coordinates of the point B =(0,4/3)
2) The equation if a line AB is x+6y-8 = 0
Used formulae:-
Section formula:-
The coordinates of the point which divides the linesegment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 is P(x,y) =
({m1x2+m2x1}/(m1+m2), {m1y2+m2y1}/(m1+m2))
Two points equation formula:-
The equation of a line passing through the points (x1, y1) and (x2, y2) is
(y-y1)/(x-x1) = (y2-y1)/(x2-x1)