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 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.
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 greater than the radius of the circle.

Explanation:

Step1: Find the radius of the circle

From the graph, the radius \(r = 6\) (distance from the center \((0,0)\) to a point on the circle, e.g., \((6,0)\))

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 \(x_1 = 0,y_1 = 0,x_2=-5,y_2 = 0\). Then \(d=\sqrt{(-5 - 0)^2+(0 - 0)^2}=\sqrt{(-5)^2}=5\)

Step3: Compare the distance and the radius

Since \(d = 5\) and \(r=6\), and \(5<6\)

Answer:

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