Question

Determine the coordiantes of the centre of a circle whose diameter has endpoints (4;-1) and (-6;7)

Answer 1

Dear Student,

Let the coordinates of centre of circle = (x, y)

Then by using mid point formula,

$$\begin{gathered} x=\frac{x_1+x_2}{2}andy=\frac{y_1+y_2}{2} \\ where(x_1,y_1)=(4,-1)and\left(x_2,y_2\right)=(-6,7) \\ Now,substitutingthesevalues,weget, \\ x=\frac{4+\left(-6\right)}{2}andy=\frac{-1+7}{2} \\ \Rightarrow x=\frac{-2}{2}andy=\frac{6}{2} \\ \Rightarrow x=-1andy=3 \end{gathered}$$

Therefore, coordinates of centre of circle = (-1, 3)

regards,