Question

2.) prove or disprove that point (4.00, 4.50) lies on circle o centered at the origin.

Explanation:

Step1: Find circle's radius

From the graph, the circle intersects the x-axis at $(6,0)$, so radius $r = 6$. The circle's equation is $x^2 + y^2 = r^2 = 36$.

Step2: Substitute point into equation

Substitute $(4.00, 4.50)$ into $x^2 + y^2$:
$4.00^2 + 4.50^2 = 16 + 20.25 = 36.25$

Step3: Compare to radius squared

$36.25
eq 36$, so the point does not satisfy the circle's equation.

Answer:

The point $(4.00, 4.50)$ does not lie on circle O centered at the origin.