Question

rs has an endpoint at r(6, - 4) and length 17. which of the following cannot be the coordinates of s? choose the correct answer below. a. (-9, -12) b. (14,11) c. (6,13) d. (23, - 4) e. (23,13)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $R(6,-4)$ is $(x_1,y_1)$ and $S(x_2,y_2)$ and $d = 17$.

Step2: Check option A

For $S(-9,-12)$, $d=\sqrt{(-9 - 6)^2+(-12+4)^2}=\sqrt{(-15)^2+(-8)^2}=\sqrt{225 + 64}=\sqrt{289}=17$.

Step3: Check option B

For $S(14,11)$, $d=\sqrt{(14 - 6)^2+(11 + 4)^2}=\sqrt{8^2+15^2}=\sqrt{64+225}=\sqrt{289}=17$.

Step4: Check option C

For $S(6,13)$, $d=\sqrt{(6 - 6)^2+(13 + 4)^2}=\sqrt{0+(17)^2}=17$.

Step5: Check option D

For $S(23,-4)$, $d=\sqrt{(23 - 6)^2+(-4 + 4)^2}=\sqrt{17^2+0}=17$.

Step6: Check option E

For $S(23,13)$, $d=\sqrt{(23 - 6)^2+(13 + 4)^2}=\sqrt{17^2+17^2}=\sqrt{2\times17^2}=17\sqrt{2}
eq17$.

Answer:

E. $(23,13)$