Question

question 16 of 20
instructions
choose the best answer. if necessary, use the paper you were given.
question
in the xy - plane, a circle has radius 4 and center at (0,0). if the radius of the circle is doubled, which of the following points will not be inside the circle?
a (3, 5)
b (5, 5)
c (6, 5)
d (6, 6)

Explanation:

Step1: Find the new radius

The original radius is 4, and it is doubled, so the new radius $r = 8$.

Step2: Use the distance - formula for a point $(x,y)$ from the origin

The distance $d$ of a point $(x,y)$ from the origin $(0,0)$ is given by the formula $d=\sqrt{(x - 0)^2+(y - 0)^2}=\sqrt{x^{2}+y^{2}}$. A point is inside the circle if $d

Step3: Calculate the distance for each option

Option A:

For the point $(3,5)$, $d_A=\sqrt{3^{2}+5^{2}}=\sqrt{9 + 25}=\sqrt{34}\approx5.83<8$.

Option B:

For the point $(5,5)$, $d_B=\sqrt{5^{2}+5^{2}}=\sqrt{25+25}=\sqrt{50}\approx7.07<8$.

Option C:

For the point $(6,5)$, $d_C=\sqrt{6^{2}+5^{2}}=\sqrt{36 + 25}=\sqrt{61}\approx7.81<8$.

Option D:

For the point $(6,6)$, $d_D=\sqrt{6^{2}+6^{2}}=\sqrt{36+36}=\sqrt{72}\approx8.49>8$.

Answer:

D. $(6,6)$