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.

Explanation:

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

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Then, given the points
`(6,5√(2))` and
`(4,3√(2))`, we can identify that:

`x_2=4\\x_1=6\\y_2=3√(2)\\y_1=5√(2)`

Now we must substitute these values into the formula:

`d=\sqrt{(4-6)^2+(3√(2)-5√(2))^2}`

We get that the distance between these two points is:

`d=2√(3)`