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Anna [14]
3 years ago
11

The distance between the two points is (2,-3)and (k,9) is 13 units find k​

Mathematics
1 answer:
docker41 [41]3 years ago
8 0

Step-by-step explanation:

\sqrt{(k - 2)^{2}  +  {(9 + 3)}^{2} }  = 13 \\  \\  \therefore \:  \sqrt{k^{2} - 2 \times 2k + 2^{2}  +  {(12)}^{2} }  = 13 \\  \\ \therefore \:  \sqrt{k^{2} - 4k + 4 +  144 }  = 13\\  \\ \therefore \:  \sqrt{k^{2} - 4k + 148 }  = 13 \:  \\  \:  \:  \:  \:  \:  \: squaring \: both \: sides \\  \\ k^{2} - 4k + 148  = 169 \\  \\ \therefore \:  k^{2} - 4k + 148   -  169  = 0\\  \\ \therefore \:  k^{2} - 4k  - 21  = 0\\  \\ \therefore \:  k^{2} - 7k  + 3k - 21  = 0\\  \\ \therefore \:  k(k - 7) + 3(k - 7)  = 0 \\  \\ \therefore \:  (k - 7) (k+ 3)  = 0 \\  \\ \therefore \:  (k - 7) = 0 \: or \:  (k+ 3)  = 0 \\  \\ \therefore \: k = 7 \: or \: k =  - 3 \\  \\  \huge \purple{ \boxed{\therefore \:k =  \{ - 3, \:  \: 7 \}}}

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