Question

If the distance between the points (k,2) and ( 3,4 ) is 8 then k=​

Answer 1

(k,2) and (3,4)

distance = 8

$distance = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1)}^{2} }$

$8 = \sqrt{(3 - k) ^{2} + {(4 - 2)}^{2} }$

$8 = \sqrt{(3 - k )^{2} + 4}$

$8 ^{2} = (3 - k) ^{2} + 4$

$64 - 4 = (3 - k)^{2}$

60= 9 + k^2 -6k

60-9 = k(k-6)

51 = k(k-6)

k=51, k=57