Question

the point (0, 5) lies on a circle that is centered at the origin. does (-3, -4) also lie on the circle? 1 identify the radius from the graph. r = units 2 determine the distance from the center to (-3, -4) using the distance formula distance = units 3 compare the radius to the distance. does the point (-3, -4) also lie on the circle? yes no

Explanation:

Step1: Find the radius

The circle is centered at the origin $(0,0)$ and the point $(0,5)$ lies on it. Using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, with $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(0,5)$, we have $r=\sqrt{(0 - 0)^2+(5 - 0)^2}=\sqrt{0 + 25}=5$.

Step2: Calculate the distance from the origin to (-3,-4)

Using the distance formula with $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-3,-4)$, we get $d=\sqrt{(-3 - 0)^2+(-4 - 0)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step3: Compare radius and distance

Since the radius $r = 5$ and the distance from the origin to $(-3,-4)$ is also $5$, the point $(-3,-4)$ lies on the circle.

Answer:

1. $r = 5$ units
2. distance $= 5$ units
3. yes