Question

18. The end points of a line segment AB are A(a, b) and B(b, a), where a and b both are positive. In what ratio the line segment AB is divided by axes?​

Answer 1

Given that, Line passes through A ( a, b), B (b, a)

$m = \frac{a - b}{b - a} = - \frac{b - a}{b - a} = - 1$

Now, The equation of the line is,

⇒ (y - b) = - ( x - a)

⇒ y - b + x + a

⇒ x + y + a - b = 0

X axis divides the line joining two points in the ratio - y₁ : y₂

So the required ratio is - b : a

Y axis divides the line joining two points

in the ratio - x₁ : x₂

So the required ratio is - a : b

Answer 2

$\huge\bold\blue{AnSweR}$

Given :-

Line passes through A ( a, b) and B (b, a)

$\sf\green{m = \frac{a - b}{b - a} = - \frac{b - a}{b - a}=-1}$

Hence, The equation of the line is,

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

= y - b + x + a

= x + y + a - b = 0

X axis divides the line joining two points in the ratio - y₁ : y₂

So the required ratio is - b : a

Y axis divides the line joining two points

in the ratio - x₁ : x₂

So the required ratio is - a : b