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

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(\left(x_1+x_2\right))/(2),(\left(y_1+y_2\right))/(2)`

By substituting the values, we will have

By equating both equations, we will have

`\begin{gathered} ((-4+x_(2)))/(2)=3 \\ -4+x_2=2*3 \\ -4+x_2=6 \\ x_2=6+4 \\ x_2=10 \end{gathered}`
`\begin{gathered} ((6+y_(2)))/(2)=5 \\ 6+y_2=2*5 \\ 6+y_2=10 \\ y_2=10-6 \\ y_2=4 \end{gathered}`

Hence,

The coordinate of B is

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