Math, asked by ruzariosequeira04, 11 months ago

Find the value of K if the point P(0,2) is equidistant from A (3,k) and B (K, 5)​

Answers

Answered by Anonymous
8

Answer:

hope it will help you:-)

Attachments:
Answered by BrainlyConqueror0901
14

\blue{\bold{\underline{\underline{Answer:}}}}

\green{\tt{\therefore{Value\:of\:k=1}}}

\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}

 \green {\underline \bold{Given :}} \\   \tt{: \implies Coordinate \: of \: P = (0,2)}  \\  \\ \tt{: \implies Coordinate \: of \: A = (3,k)}  \\  \\ \tt{: \implies Coordinate \: of \: B = (k,5)}  \\  \\ \red{\underline \bold{To \: Find :}}  \\  \tt{:  \implies Value \: of \: k = ?}

• According to given question :

\text{P\:is\:equidistant\:from\:A\:and\:B}\\\text{Then,} \\\\\bold{As \: we \: know \: that} \\  \tt{:  \implies AP= BP } \\  \\   \tt{: \implies  \sqrt{(0-3)^{2}+(2-k)^{2}}= \sqrt{(0-k)^{2}+(2-5)^{2}} } \\  \\  \tt{:  \implies 3 + k = 0} \\  \\  \tt{:  \implies (-3)^{2}+4+k^{2}-4k =  (-k)^{2}+(-3)^{2}} \\ \\  \tt{:\implies 9-9+k^{2}-k^{2}-4k+4=0}\\ \\   \tt{:  \implies 4-4k = 0  } \\  \\   \tt{: \implies 4= 4k } \\  \\  \tt{:  \implies k=\frac{4}{4}} \\  \\  \green{\tt{:  \implies k =   1}}

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