Question

AB is a diameter of a circle, where A(-3,-4) and B(3,4). Find its centre and length of diameter.

• A. $\begin{array}{c}centre=(0,4)\\ radius=19cm\end{array}$
• B. $\begin{array}{c}centre=(0,0)\\ radius=10cm\end{array}$
• C. $\begin{array}{c}centre=(5,5)\\ radius=8cm\end{array}$
• D. $\begin{array}{c}centre=(-8,4)\\ radius=20cm\end{array}$

Answer 1

The correct option is B

$\begin{array}{c}centre=(0,0)\\ radius=10cm\end{array}$

Let O be the centre of the circle and A(-3,-4)and B(3,4) are the two and points of the diameter AB, of the circle.

$\because$ O is the midpoint of AB

$\therefore x=\frac{-3+3}{2}=0$

$y=\frac{4-4}{2}=0$

Centre O(x,y) = O(0,0)

Length of diameter.

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

$=\sqrt{\left(3\right)-(-3{)}^2+(4-(-4){)}^2}=\sqrt{6^2+8^2}$

$=\sqrt{{10}^2}=10cm$