Question

Does the point (1, StartRoot 7 EndRoot) lie on the circle shown? Explain. Yes, the distance from (–2, 4) to (–2, 0) is 4 units. Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units. No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units. No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.

Answer 1

Answer:

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

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the equation of the circle

we know that

The equation of the circle is equal to

$(x-h)^{2}+(y-k)^{2} =r^{2}$

where

(h,k) is the center

r is the radius

In this problem we have

$(h,k)=(-2,0)$

and the radius is equal to the distance between the center and the point (-2,4)

so

$r=4\ units$ ----> look at the graph

substitute in the equation

$(x+2)^{2}+(y)^{2} =4^{2}\\(x+2)^{2}+(y)^{2} =16$

step 2

If the distance between the center and the point is equal to the radius of the circle , then the point lie on the circle

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

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}\\A(-2,0)\\B(1,\sqrt{7})$

substitute the values

$d=\sqrt{(\sqrt{7}-0)^{2}+(1+2)^{2}}\\d=\sqrt{7+9}\\d=\sqrt16}=4\ units$

therefore

the point lie on the circle

Answer 2

Answer: B

Step-by-step explanation: