if (x,y) is any point on the lines joining the points capital A(a,0)and B(0,b) then show that x/a+y/b= 1 .
Answers
Step-by-step explanation:
Given :-
(x,y) is any point on the lines joining the points A(a,0)and B(0,b) .
To find :-
Show that x/a+y/b= 1 .
Solution :-
Given points are A(a,0) and B(0,b)
Let (x1, y1) = (a,0) => x1 = a and y1 = 0
Let (x1, y2) = (0,b) => x2 = 0 and y2 = b
(x,y) is any point on the linesegment joining the points A and B
We know that
If (x,y) lies on the linesegment joining the points (x1,y1) and (x2,y2) then the equation of a line is
(y-y1)/(x-x1) = (y2-y1)/(x2-x1)
On Substituting these values in the above formula then
=>(y-0)/(x-a) = (b-0)/(0-a)
=> y/(x-a) = b/-a
=> y/(x-a) = -b/a
On applying cross multiplication then
=> a×y = (x-a)×-b
=> ay = (-b×x) -(a×-b)
=> ay = -bx -(-ab)
=> ay = -bx + ab
=> ay+bx = ab
On dividing by ab both sides then
=> (ay+bx)/ab = ab/ab
=> (ay+bx)/ab = 1
=> (ay/ab) +(bx/ab) = 1
=> (y/b) +(x/a) = 1
=> (x/a) + (y/b) = 1
Hence Proved.
Answer:-
If (x,y) is any point on the lines joining the points A(a,0)and B(0,b) then x/a+y/b= 1
Used formulae:-
If (x,y) lies on the linesegment joining the points (x1,y1) and (x2,y2) then the equation of a line is
(y-y1)/(x-x1) = (y2-y1)/(x2-x1).
