Question

Distance formula: Vx2 - x1)? + (V2 - 7)? Does the point (2. 6) lie on the circle shown? Explain.

Answer 1

Option D: No, the distance from $(0,0)$ to $(2, \sqrt{6})$ is not 3 units.

Explanation:

From the figure, we can see that the radius of the circle is 3 units.

We need to determine that the point $(2, \sqrt{6})$ lie on the circle.

This can be determined by substituting the coordinate $(0,0)$ and $(2, \sqrt{6})$ in the distance formula,

$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Thus, we get,

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

Simplifying, we have,

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

$d=\sqrt{6+4}$

$d=\sqrt{10}$

$d=3.2$

Thus, the distance from $(0,0)$ to $(2, \sqrt{6})$ is 3.2 units.

Hence, the point $(2, \sqrt{6})$ does not lie on the circle because the distance is more than the radius 3 units.

Therefore, the distance from $(0,0)$ to $(2, \sqrt{6})$ is not 3 units.

Thus, Option D is the correct answer.