Question

for what value of k distance between the points 5.-2 and k 4 is 10 units

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Answer 1

Answer:

k=13 or k=-3

Step-by-step explanation:

Distance formula = $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Distance between (5,-2) and (k,4)

$=\sqrt{(5-k)^2+(-2-4)^2}\\\\=\sqrt{25+k^2-10k +36}\\\\=\sqrt{61+k^2-10k}$

= 10 units

Thus,

$\sqrt{61+ k^2 - 10k} = 10\\Squaring,\\61+ k^2 - 10k=100\\ k^2 - 10k-39=0\\k=13 \\or\ k=-3$