Question

a circle has a center (3,5) and a diameter AB. The coordinates of A are (-4,6). what are the coordinates of B?

Answer 1

Answer:

The question can be explained using the image below

The given coordinates are

$\begin{gathered} A\left(-4,6\right)\Rightarrow\left(x_1,y_1\right) \\ C\left(3,5\right)\Rightarrow\left(x,y\right) \\ B\left(x_2,y_2\right)\Rightarrow \end{gathered}$

The center is the midpoint of Diameter AB, therefore, we will use the formula for the midpoint of a line given below as

$\left(x,y\right)\Rightarrow\frac{\left(x_1+x_2\right)}{2},\frac{\left(y_1+y_2\right)}{2}$

By substituting the values, we will have

$\begin{gathered} (x,y)\operatorname{\Rightarrow}\frac{(x_{1}+x_{2})}{2}, \frac{(y_{1}+y_{2})}{2} \\ \left(3,5\right)\Rightarrow\frac{\left(-4+x_2\right)}{2},\frac{\left(6+y_2\right)}{2} \end{gathered}$

By equating both equations, we will have

$\begin{gathered} \frac{(-4+x_{2})}{2}=3 \\ -4+x_2=2\times3 \\ -4+x_2=6 \\ x_2=6+4 \\ x_2=10 \end{gathered}$$\begin{gathered} \frac{(6+y_{2})}{2}=5 \\ 6+y_2=2\times5 \\ 6+y_2=10 \\ y_2=10-6 \\ y_2=4 \end{gathered}$

Hence,

The coordinate of B is

$\Rightarrow\left(10,4\right)$