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. (23,13) b. (6,13) c. (-9, - 12) d. (23, - 4) e. (14,11)

Question

Accepted Answer

# Explanation:
## Step1: Recall distance formula
The distance formula between two points $R(x_1,y_1)$ and $S(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1 = 6,y_1=-4$ and $d = 17$.
## Step2: Check option A
For $S(23,13)$:
$$
\begin{align*}
d&=\sqrt{(23 - 6)^2+(13+ 4)^2}\
&=\sqrt{17^2+17^2}\
&=\sqrt{2\times17^2}\
&=17\sqrt{2}
eq17
\end{align*}
$$
## Step3: Check option B
For $S(6,13)$:
$$
\begin{align*}
d&=\sqrt{(6 - 6)^2+(13 + 4)^2}\
&=\sqrt{0+17^2}\
&=17
\end{align*}
$$
## Step4: Check option C
For $S(-9,-12)$:
$$
\begin{align*}
d&=\sqrt{(-9 - 6)^2+(-12 + 4)^2}\
&=\sqrt{(-15)^2+(-8)^2}\
&=\sqrt{225 + 64}\
&=\sqrt{289}\
&=17
\end{align*}
$$
## Step5: Check option D
For $S(23,-4)$:
$$
\begin{align*}
d&=\sqrt{(23 - 6)^2+(-4 + 4)^2}\
&=\sqrt{17^2+0}\
&=17
\end{align*}
$$
## Step6: Check option E
For $S(14,11)$:
$$
\begin{align*}
d&=\sqrt{(14 - 6)^2+(11 + 4)^2}\
&=\sqrt{8^2+15^2}\
&=\sqrt{64+225}\
&=\sqrt{289}\
&=17
\end{align*}
$$
# Answer:
A. $(23,13)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall distance formula

Step2: Check option A

Step3: Check option B

Step4: Check option C

Step5: Check option D

Step6: Check option E

Answer: