Question

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 :-

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

$\sf\pink{m = \sf \dfrac{a - b}{b - a} = - \sf \dfrac{b - a}{b - a}=-1}$

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

Answer 2

Answer:

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

\sf\pink{m = \sf \dfrac{a - b}{b - a} = - \sf \dfrac{b - a}{b - a}=-1}m=

b−a

a−b

=−

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