Question

if p(x,y) is a point on line joining A(a,0) and B(0,b) then prove that x/a + y/b=1
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Answer 1

Answer:

hey dear there are two methods to do this question (decide which one u can understand)

method1

Using the slope form of the line,

(y - 0)/(x - a) = (b - y)/(0 - x) ..........(Slope between P and A must be equal to the slope between B and P)

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

(b - y)(x - a)/(-xy) = 1

(bx - ab - xy + ay)/(-xy) = 1

1 + ab/(xy) - b/y - a/x = 1

ab/(xy)  =  b/y + a/x

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

x/a + y/b = 1

or

method2

Given that the point P (x, y) lies on the line joining the points A (a, 0) and B (0, b)

Thus, the points A (a, 0), P (x, y) and B (0, b) are collinear points

The area of the triangle formed between these three points is zero