Question

find the distance of the line segment joining the two points (-4 /2 - /12) and (/32, 2/3)

Answer 1

Answer: $4\sqrt{3}$ .

Step-by-step explanation:

Distance formula : Distance between points (a,b) and (c,d) is given by :-

$D=\sqrt{(d-b)^2+(b-a)^2}$

Distance between points $(-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})$.

$D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}$

Hence, the correct option is $4\sqrt{3}$ .