Question

A circle is centered at T(-6,3)T(−6,3)T, left parenthesis, minus, 6, comma, 3, right parenthesis and has a radius of 111111.

Where does the point N(3,-3)N(3,−3)N, left parenthesis, 3, comma, minus, 3, right parenthesis lie?

Answer 1

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Answer 2

The point N lies inside the circle

Explanation:

A circle is centered at the point T(-6,3) and has a radius of r=1.

To determine if the point N(3,-3) is inside or outside the circle, the distance between N and the point T must be lower than 11.

To calculate the distance between points T and N you use:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

where x1 and y1 are the coordinates of T, and x2 and y2 the coordinates of N.

`d=√((3-(-6))^2+(-3-3)^2)=√(9^2+6^2)=10.81`

d < 11

The distance d is lower than the radius of the circle. Hence, the point N lies inside the circle