Question

The endpoints of the diameter of a circle are(2,4) &(-3,-1). find its centre.​

Answer 1

Answer:

$(-0.5, 1.5)$

Step-by-step explanation:

Given:-

The endpoints of the diameter of a circle are (2, 4) and (-3, -1)

To find:-

The centre of the circle

Solution:-

Let the coordinates of the centre of the circle be O $(x,y)$.

$x_{1}=2, x_{2}=-3, y_{1}=4, y_{2}=-1$

We know, that the midpoint of every diameter is the centre of the respective circle.

So, by using midpoint formula,

$(x=\frac{x_{1}+x_{2}}{2}, y=\frac{y_{1}+y_{2}}{2})$

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

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

⇒ $(\frac{2-3}{2},\frac{4-1}{2})$

⇒ $(\frac{-1}{2},\frac{3}{2})$

⇒ $(-0.5, 1.5)$

∴ The coordinates of the centre of the circle is $(-0.5, 1.5)$.