Question

a circle is centered at c(-1, -3) and has a radius of 6. where does the point p(-6, -6) lie? choose 1 answer: a inside the circle b on the circle c outside the circle

Explanation:

Step1: Calculate distance between center and point

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $(x_1,y_1)=(-1,-3)$ (center $C$) and $(x_2,y_2)=(-6,-6)$ (point $P$).
$d=\sqrt{(-6 - (-1))^2+(-6 - (-3))^2}$

Step2: Simplify the expression

$d=\sqrt{(-5)^2+(-3)^2}=\sqrt{25 + 9}=\sqrt{34}\approx 5.83$

Step3: Compare distance with radius

Radius $r = 6$, and $d\approx5.83<6$.

Answer:

A. Inside the circle