Question

what is a centre of the circle if two of its points are A(3,0) and B(-1,4)​

Answer 1

Answer:

$\bold\red{Centre= (1,2)}$

Step-by-step explanation:

Given,

A(3,0) and B(-1,4) are the ends of diameter.

Now,

we know that,

Diameter of a cirlce passes through the centre.

Also,

Center divides the diameter into two equal parts.

Therefore,

Centre is the midpoint of diameter AB.

Now,

we know that,

If (a,b ) and (c, d) are the ends of a line segment,

then ,

it's mid point is given by $\bold{(\frac{a+c}{2},\frac{b+d}{2})}$

Therefore,

Centre of the circle is

$={(\frac{3-1}{2},\frac{0+4}{2})}$

$={(\frac{2}{2},\frac{4}{2})}$

Hence,

$\bold{Centre= (1,2)}$