Question

circle q is centered at the origin. is point (-5, 0) on the circle? justify your answer.
○ yes because the distance from the origin to point (-5, 0) is equal to the radius of the circle.
○ no because the distance from the origin to point (-5, 0) is less than the radius of the circle.
○ yes because the distance from the origin to point (-5, 0) is greater than the radius of the circle.
○ no because the distance from the origin to point (-5, 0) is greater than the radius of the circle.

Explanation:

Step1: Identify circle radius

From the graph, the circle centered at the origin passes through $(6,0)$, so radius $r=6$.

Step2: Calculate distance from origin to $(-5,0)$

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d=\sqrt{(-5-0)^2+(0-0)^2}=\sqrt{25}=5$

Step3: Compare distance and radius

$5 < 6$, so the point is inside, not on the circle.

Answer:

No because the distance from the origin to point (-5, 0) is less than the radius of the circle.