the circle shown below is centered at the origin and contains the point (-4,-2). Which of the following is closest to the length of the diameter of the circle?

Accepted Solution

we know the circle has its center at the origin, 0,0, and the point -4,-2 is on the circle, is just the distance from the center to a point on it, thus

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{ -4}}\quad ,&{{ -2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{(-4-0)^2+(-2-0)^2}\implies r=\sqrt{(-4)^2+(-2)^2} \\\\\\ r=\sqrt{16+4}\implies r=\sqrt{20}\implies r=\sqrt{4\cdot 5}\implies r=\sqrt{2^2\cdot 5} \\\\\\ r=2\sqrt{5}[/tex]