Question

the center of a circle on a cordinate plane is located at the point (2,-1). one endpoint of the diameter is located (0,-2). what are the coordinates of the other endpoint of the diamtere of the circle

Answer 1

check the picture below

so... the center coordinates of the circle, are the Midpoint of both ends, thus we can simply use the MidPoint equation to get it

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ -1}})\quad % (c,d) &({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{2+x}{2}\quad ,\quad \cfrac{-1+y}{2} \right)=(0,-2)\implies \begin{cases} \frac{2+x}{2}=0\\ 2+x=0\\ \boxed{x=-2}\\ -------\\ \frac{-1+y}{2}=-2\\ -1+y=-4\\ \boxed{y=-3} \end{cases}$