Math, asked by ag37475768, 10 months ago

Find the value of k if the distance between the points (2,k) and (4,3) is 8. full solution step by step

Answers

Answered by Sharad001
101

Question :-

Find the value of k if the distance between the points (2,k) and (4,3) is 8 .

Answer :-

\to \boxed{ \rm k = 3 - 4 \sqrt{15} } \:

To Find :-

→ Value of k

Used Formula :-

 \rm if \: we \: have \: two \: points \: (x_1,y_1) and \\  \rm (x_2,y_2)  \: then \: distance \: between \: them \: is \\  \\  \to \rm distance =  \sqrt{ {(x_2 - x_1)}^{2} +  {  (y_2 - y_1)}^{2}  }

Step - by - step explanation :-

According to the question,

→ Distance between the points (2,k) and (4,3) is 8 units .

Hence ,

 \implies  \rm(2,k) \to  x_1 = 2,y_1 = k \\  \\  \implies \rm (4,3)  \to x_2 = 4,y_2 = 3 \:  \\ \\   \rm \: distance \:  = 8 \: units \\ \rm \red{ now \: apply \: the \: given \: formula} \\  \\   \to \rm 8 =  \sqrt{ {(4 - 2)}^{2}  +  {(3 - k)}^{2} }  \\  \\  \sf \green{ squaring \: on \: both \: sides} \\  \\  \to \rm {(8)}^{2}  =  { \bigg \{ \sqrt{ {(2)}^{2}  +  {(3 - k)}^{2} } \bigg \} }^{2}  \\  \\  \to \rm 64 = 4 +  {(3 - k)}^{2}  \\  \\  \to \rm 64 - 4 =  {(3 - k)}^{2}  \\  \\  \to \rm  60 =  {(3 - k)}^{2}  \\   \\   \rm \: taking \:  \sqrt{}  \: on \: both \: sides \\  \\  \to \rm \sqrt{60}  =  \sqrt{ {(3 - k)}^{2} }  \\  \\  \to \rm 4\sqrt{15}  = 3 - k \\  \\  \to \boxed{ \rm k = 3 - 4 \sqrt{15} }

Answered by savitayenorkar86
2

-Answer :-

\to \boxed{ \rm k = 3 - 4 \sqrt{15} } \:→

k=3−4

15

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