Question

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

Explanation:

Step1: Determine the radius of the circle

By observing the graph, the circle intersects the x - axis at approximately $x = 6$ and $x=-6$, so the radius $r = 6$.

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

Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-5,0)$. Then $d=\sqrt{(-5 - 0)^2+(0 - 0)^2}=\sqrt{(-5)^2}=\sqrt{25}=5$.

Step3: Compare the distance and the radius

Since $5<6$ (distance $d = 5$ and radius $r = 6$), the point $(-5,0)$ is inside the circle.

Answer:

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