Question

select the correct answer. which point lies on a circle with a radius of 5 units and center at p(6, 1)? a. q(1, 11) b. r(2, 4) c. s(4, -4) d. t(9, -2)

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For a point to be on a circle with center $(x_0,y_0)$ and radius $r$, the distance between the point $(x,y)$ and the center $(x_0,y_0)$ should be equal to $r$. Here, $x_0 = 6,y_0=1,r = 5$.

Step2: Check option A

For point $Q(1,11)$, $d_Q=\sqrt{(1 - 6)^2+(11 - 1)^2}=\sqrt{(-5)^2+10^2}=\sqrt{25 + 100}=\sqrt{125}
eq5$.

Step3: Check option B

For point $R(2,4)$, $d_R=\sqrt{(2 - 6)^2+(4 - 1)^2}=\sqrt{(-4)^2+3^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step4: Check option C

For point $S(4,-4)$, $d_S=\sqrt{(4 - 6)^2+(-4 - 1)^2}=\sqrt{(-2)^2+(-5)^2}=\sqrt{4 + 25}=\sqrt{29}
eq5$.

Step5: Check option D

For point $T(9,-2)$, $d_T=\sqrt{(9 - 6)^2+(-2 - 1)^2}=\sqrt{3^2+(-3)^2}=\sqrt{9+9}=\sqrt{18}
eq5$.

Answer:

B. $R(2,4)$