Question

If p(x,y) is any point on the line segment joining the points (a,0) and (0,6) then prove that x/a+ y/b =1​

Answer 1

Step-by-step explanation:

Given Question :-

If p(x,y) is any point on the line segment joining the points (a,0) and (0,6) then prove that x/a+ y/b =1

Correct Question :-

If p(x,y) is any point on the line segment joining the points (a,0) and (0,b) then prove that x/a+ y/b =1

Solution :-

Given points are (a,0) and (0,b)

Let A(x1, y1)= (a,0)=> x1= a and y1 = 0

Let B =(0,b) = (0,b)=> x2 = 0 and y2 = b

P(x,y) is any point on the line segment joining the given points

We know that

If a point (x,y) is on the linesegment joining the points (x1, y1) and (x2, y2) then the equation of the line is (y-y1)/(x-x1) = (y2-y1)/(x2-x1)

Given that

P(x,y) is any point on the line segment joining the given points (a,0) and (0,b) then

On Substituting these values in the above formula then

=> (y-0)/(x-a) = (b-0)/(0-a)

=> y / (x-a) = b /-a

On applying cross multiplication then

=> (x-a)(b) = y(-a)

=> bx -ab = -ay

=> bx + ay = ab

On dividing by ab both sides then

=> (bx/ab) + (ay/ab) = (ab/ab)

=> (x/a) + (y/b) = 1

Hence, Proved.

Answer:-

If p(x,y) is any point on the line segment joining the points (a,0) and (0,b) then x/a+ y/b =1.

Used formulae:-

If a point (x,y) is on the linesegment joining the points (x1, y1) and (x2, y2) then the equation of the line is (y-y1)/(x-x1) = (y2-y1)/(x2-x1)