Question

a circle in the xy - plane has its center at the point (-6,1). if the point (7,12) lies on the circle, what is the radius of the circle? (round the answer to the nearest integer.) show calculator how do i enter a student - produced response on the sat? show me!

Explanation:

Step1: Recall distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. The radius of the circle is the distance between the center $(-6,1)$ and the point on the circle $(7,12)$. Here $x_1=-6,y_1 = 1,x_2=7,y_2 = 12$.

Step2: Substitute values into formula

$d=\sqrt{(7-(-6))^2+(12 - 1)^2}=\sqrt{(7 + 6)^2+(11)^2}=\sqrt{(13)^2+121}=\sqrt{169 + 121}=\sqrt{290}$.

Step3: Calculate and round

$\sqrt{290}\approx17$.

Answer:

17