Question

Does the point (1, 7) lie on the circle shown?

Answer 1

Answer:

the answer is b

Step-by-step explanation:

Answer 2

Answer:

Yes, the distance from $(-2,0)\ to\ (1,\sqrt{7})$ is 4 units

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center and any point that lie on the circle is equal to the radius of the circle

In this problem we have

the center is (-2,0)

Find the distance between (-2,0) and (-2,4)

the formula to calculate the distance between two points is equal to

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

substitute

$r=\sqrt{(4-0)^{2}+(-2+2)^{2}}$

$r=\sqrt{(4)^{2}+(0)^{2}}$

$r=4\ units$

step 2

Verify if the point $(1,\sqrt{7})$ lie on the circle

Find the distance between the center and the given point and compare the result with the value of the radius

we have

$(-2,0),(1,\sqrt{7})$

substitute in the formula

$d=\sqrt{(\sqrt{7}-0)^{2}+(1+2)^{2}}$

$d=\sqrt{(\sqrt{7})^{2}+(3)^{2}}$

$d=\sqrt{16}$

$d=4\ units$

The distance is equal to the radius

therefore

The point $(1,\sqrt{7})$ lie on the circle