Question

a circle is centered at o(0, 0) and has a radius of $2\sqrt{3}$. where does the point m(-3, 2) lie? choose 1 answer: a inside the circle b on the circle c outside the circle

Explanation:

Step1: Calculate distance from O to M

The distance \( d \) between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Here, \( O(0,0) \) and \( M(-3,2) \), so \( d=\sqrt{(-3 - 0)^2+(2 - 0)^2}=\sqrt{9 + 4}=\sqrt{13} \).

Step2: Calculate radius squared

The radius \( r = 2\sqrt{3} \), so \( r^2=(2\sqrt{3})^2 = 12 \).

Step3: Compare distance squared and radius squared

\( d^2 = 13 \) and \( r^2 = 12 \). Since \( d^2>r^2 \), the distance from \( O \) to \( M \) is greater than the radius.

Answer:

C. Outside the circle