Question

If the distance between A(2,3) and B(K,1) is 2√2,find the value of K

Answer 1

aloha user!
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the distance between A(2,3) and B(K,1) is given to be 2√2.
we are gonna use distance formula.

x1= 2
x2 = k
y1 = 3
y2 = 1
                   
distance= √(x2 - x1)² + (y2 - y1)
            
2√2 = √ ( k - 2 )² + (1 - 3 )²
             
2√2 = √ k² + 4 - 4k + 4

(2√2)² = k² - 4k +8

4 × 2 = k² - 4k + 8

8 = k² -4k + 8

0 = k² - 4k

0 = k ( k - 4 )

0 = k - 4 

k = 4
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hope it helps :^)