Question

the endpoints of the diameter of a circle are P(-7, -4) and Q(-1, 10). Find the coordinates of the centre of this circle

Answer 1

if the endpoints of the diameter chord are P and Q, then the center must be in middle of that diameter, namely the midpoint of PQ.


`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{-7}~,~\stackrel{y_1}{-4})\qquad Q(\stackrel{x_2}{-1}~,~\stackrel{y_2}{10}) \qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-1-7}{2}~~,~~\cfrac{10-4}{2} \right)\implies \left( \cfrac{-8}{2}~~,~~\cfrac{6}{2} \right)\implies (-4~,~3)`