Answer:
The point not lie on the circle, because the distance from (0, 0) to (2, square root 6 ) is not 3 units.
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The distance from the center of the circle to any point on the circle, must be equal to the radius of the circle
In this problem
The center of the circle is the point (0,0)
The radius of the circle is r=3 units
step 1
Find out the distance between the center and the given point
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex](0,0)[/tex] and [tex](2,\sqrt{6})[/tex]
substitute in the formula
[tex]d=\sqrt{(\sqrt{6}-0)^{2}+(2-0)^{2}}[/tex]
[tex]d=\sqrt{(\sqrt{6})^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{10}\ units[/tex]
so
[tex]\sqrt{10}\ units\neq 3\ units[/tex]
therefore
The point not lie on the circle, because the distance from (0, 0) to (2, square root 6 ) is not 3 units.
Answer: No, the distance from (0,0) to (2 , square root 6) is not 3 units .
Step-by-step explanation: just took the test have a beautiful day lovelies
