Circle O is centered on the origin with a diameter of 14 units. Since the distance between the center and the point is 7units. So, the point lies in the circle.
What is the distance between two points ( p,q) and (x,y)?
The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
We have been given a Circle centered on the origin, (0, 0)
Radius = 7units
In order to find if the point lies on the circle, check if the distance from the center to the point is 7units.
(x, y) = (0, 0)
(p, q) = (-3,2√10)
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
[tex]D = \sqrt{(0-(-3))^2 + (0-2\sqrt{10} )^2} \: \rm units.\\\\D = \sqrt{9+ 40} \\\\D = \sqrt{49} \\\\D = 7[/tex]
Since the distance between the center and the point is 7units. So, the point lies on the circle.
Learn more about the distance between two points here:
brainly.com/question/16410393
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