Question

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

Answer 1

Answer:

distance formula =

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

therefore,

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

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

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

$9 + k {}^{2} - 6k + 4 = 16$

$k {}^{2} - 6k + 13 = 16$

${k}^{2} - 6k + 13 - 16 = 0$

${k }^{2} - 6k - 3 = 0$

after splitting the middle term, you will get the value of k