# Math Help - centre semi circle

1. ## centre semi circle

Hello
if y= squareroot R^2 -x^2
how does that justify the centre coordinates is (0,0) ?
someone explain please

2. Originally Posted by wolfhound
Hello
if y= squareroot R^2 -x^2
how does that justify the centre coordinates is (0,0) ?
someone explain please
Hi wolfhound,

Remember the "distance formula" ?

$distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^3}$

This is Pythagoras' Theorem using co-ordinates.

Just as on a clock, the hands are pivoted at the centre,
the hands are always the same length, but the point moves around the clock circumference. The circle circumference is the set of all points that are the same distance from the centre.

If the centre co-ordinates are (0,0), this reduces to

$r=\sqrt{(x_2-0)^2+(y_2-0)^2}$

$r=\sqrt{x^2+y^2}$

$r^2=x^2+y^2$

$y^2=r^2-x^2$

$y=\sqrt{r^2-x^2}$

3. Hi Archie
Great explanation, Thanks!