Mathematics: Does the point (2, StartRoot 6 EndRoot) lie on the circle shown? Explain.

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Does the point (2, StartRoot 6 EndRoot) lie on the

ashleymarie11142

18.01.2022

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

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

(0,0) and $(2,\sqrt{6})$

substitute in the formula

$d=\sqrt{(\sqrt{6}-0)^{2}+(2-0)^{2}}$

$d=\sqrt{(\sqrt{6})^{2}+(2)^{2}}$

$d=\sqrt{10}\ units$

$\sqrt{10}\ units\neq 3\ units$

therefore

The point not lie on the circle, because the distance from (0, 0) to (2, square root 6 ) is not 3 units.

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