Question

Find the distance between points (6,5 sqaure root 2) and 4,square root 3).


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Answer 1

For this case we have that by definition, the distance between two points is given by:

$d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}$

We have the following points:

$(6,5 \sqrt {2})\\(4,3 \sqrt {2})$

Substituting:

$d = \sqrt {(4-6) ^ 2 + (3 \sqrt {2} -5 \sqrt {2}) ^ 2}\\d = \sqrt {(- 2) ^ 2 + (- 2 \sqrt {2}) ^ 2}\\d = \sqrt {4+ (4 * 2)}\\d = \sqrt {4 + 8}\\d = \sqrt {12}\\d = \sqrt {2 ^ 2 * 3}\\d = 2 \sqrt {3}$

Answer:

Option C

Answer 2

Answer: Third option.

Step-by-step explanation:

The distance between two points can be calculated with this formula:

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

Then, given the points $(6,5\sqrt{2})$ and $(4,3\sqrt{2})$, we can identify that:

$x_2=4\\x_1=6\\y_2=3\sqrt{2}\\y_1=5\sqrt{2}$

Now we must substitute these values into the formula:

 $d=\sqrt{(4-6)^2+(3\sqrt{2}-5\sqrt{2})^2}$

We get that the distance between these two points is:

$d=2\sqrt{3}$