# If a+b=8 then what is the equation of the locus of a moving point which is always mid-point of (a,0) and (0,b) ?

##### 1 Answer
Sep 11, 2017

Desired locus is $y = 4 - x$

#### Explanation:

Let the movving point be $\left(x , y\right)$.

As it is the midpoint of $\left(a , 0\right)$ and $\left(0 , b\right)$

or $\left(a , 0\right)$ and $\left(0 , 8 - a\right)$, we have

$x = \frac{a}{2}$ and $y = \frac{8 - a}{2} = 4 - \frac{a}{2}$

Eliminating $a$ we have

$y = 4 - x$, which is the desired locus.