Question

PLEASE HELP ME!!!

(Khan Academy question)

A circle is centered at A(-5,-8). The point M(-1,-3) is on the circle. Where does the point V(-11,-6) lie?


(Option A)

Inside the circle


(Option B)

Outside the circle


(Option C)

On the circle

Answer 1

Option A) Inside the circle

Explanation:

step 1

Find the radius of the circle

we know that

The radius is equal to the distance from the center to any point on the circle

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

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

we have

A(-5,-8),M(-1,-3)

substitute the values

`r=\sqrt{(-3+8)^(2)+(-1+5)^(2)}`

`r=\sqrt{(5)^(2)+(4)^(2)}`

`r=√(41)\ units`

step 2

Find the distance from the center to point V

we know that

If the distance from the center to point V is equal to the radius, then the point V lie on the circle

If the distance from the center to point V is less than the radius, then the point V lie inside the circle

If the distance from the center to point V is greater than the radius, then the point V lie outside the circle

we have

A(-5,-8),V(-11,-6)

substitute in the formula

`d=\sqrt{(-6+8)^(2)+(-11+5)^(2)}`

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

`d=√(40)\ units`

so

`√(40)\ units< √(41)\ units`

The distance from the center to point V is less than the radius

therefore

The point V lie inside the circle