Q: 18        P(a,b)  is the mid-point of a line segment between axes.  Show that equation
                  of the line is  \frac{x}{a}+\frac{y}{b}=2.

Answers (1)
G Gautam harsolia

Now, let coordinates of point A is (0 , y) and of point B is (x , 0)
\frac{x+0}{2}= a \ and \ \frac{0+y}{2}= b
x= 2a \ and \ y = 2b
Therefore, the coordinates of point A is (0 , 2b) and of point B is (2a , 0)
Now, slope of line passing through points (0,2b) and (2a,0) is
m = \frac{0-2b}{2a-0} = \frac{-2b}{2a}= \frac{-b}{a}
Now, equation of line passing through point (2a,0) and with slope  \frac{-b}{a}  is
(y-0)= \frac{-b}{a}(x-2a)
\frac{y}{b}= - \frac{x}{a}+2
\frac{x}{a}+\frac{y}{b}= 2
Hence proved