Does the point (1,√3) lie inside outside or on the circle with a center at the origin containing the point (3,0)? Question 2 options: Inside On Outside

Point lies inside the circle.

Step-by-step explanation:

To determine the point which lies outside the circle, calculate the distance between the points and compare that value with radius of circle.

If d<r point lies inside the circle, d>r point lies outside circle and d=r point is on the circle.  

Let O be the center of origin of the circle. So, .  

Also given that circle contain point . So,

Now equation of circle having center (h,k) is given by the equation,

Substituting the value,

Now calculate the distance between point and .

Distance formula between points and is given as,

Now,

Simplifying,

Since r = 3 and d = 2.64. That is, d < r.

So point lies inside the circle.

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)