Answer:
k = -3
k =5
Step-by-step explanation:
\begin{gathered}d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\\end{gathered}
d=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
d=5
(−1,1)=(x
1
,y
1
)
(2,k)=(x
2
,y
2
)
\begin{gathered}5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\\end{gathered}
5=
(2−(−1))
2
+(k−1)
2
Squarebothsides:25=k
2
−2k+10
25=k
2
−2k+10
Solve25=k
2
−2k+10:
k
2
−2k+10=25
Subtract25frombothsides
k
2
−2k+10−25=25−25
k
2
−2k−15=0
Solvebyfactoring
Factork
2
−2k−15:(k+3)(k−5)
Solvek+3=0:k=−3
\begin{gathered}\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3\end{gathered}
Solvek−5=0:k=5
k=5,k=−3
Step-by-step explanation:
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