To determine which point lies on a circle with a radius of 5 units, we can use the equation of a circle centered at the origin \(\((0, 0)\)\), which is:
\(\[ x^2 + y^2 = r^2 \]\)
Here, \(\( r = 5 \)\), so the equation becomes:
\(\[ x^2 + y^2 = 25 \]\)
We'll evaluate each point to see which one satisfies this equation.
Point Q(1, 11):
\(\[ x = 1, \; y = 11 \]\)
\(\[ 1^2 + 11^2 = 1 + 121 = 122 \]\)
This does not equal 25, so Q(1, 11) is not on the circle.
Point R(2, 4):
\(\[ x = 2, \; y = 4 \]\)
\(\[ 2^2 + 4^2 = 4 + 16 = 20 \]\)
This does not equal 25, so R(2, 4) is not on the circle.
Point S(4, -4):
\(\[ x = 4, \; y = -4 \]\)
\(\[ 4^2 + (-4)^2 = 16 + 16 = 32 \]\)
This does not equal 25, so S(4, -4) is not on the circle.
Point T(9, -2):
\(\[ x = 9, \; y = -2 \]\)
\(\[ 9^2 + (-2)^2 = 81 + 4 = 85 \]\)
This does not equal 25, so T(9, -2) is not on the circle.
Based on our calculations, none of the given points lie on the circle with a radius of 5 units. So the correct answer is:
None of the points lie on the circle.
