Question

HELPP please ??? I’ll appreciate it a lot .

Answer 1

The distance between the two points provided is:
`√(41)`

Explanation:

First thing is to evaluate what the distance formula is:

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

Then substitute the points provided:

d =
`\sqrt{(7-2)^(2)+(-5-(-1)^(2) }`

(The double negative between -5 and -1 will make the -1 a positive 1). (1)

d =
`\sqrt{(5)^(2)+(6)^(2) }`

Now the exponents:

d =
`√(25+36)`

Second to last, you must add:

d =
`√(41)`

If needed ± should be added in front of the radical.

The points are the same as the ones that were given.

Answer 2

Answer:
`√(41)`

On a keyboard you would type sqrt(41)

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Work Shown:

`\text{point L} = (x_1, y_1) = (2,-1)\\\\\text{point N} = (x_2, y_2) = (7,-5)\\\\`

`d = \text{distance from L to N}\\\\d = √( (x_1-x_2)^2 + (y_1-y_2)^2 ) \ \text{ ... distance formula}\\\\d = √( (2-7)^2 + (-1-(-5))^2 )\\\\d = √( (2-7)^2 + (-1+5)^2 )\\\\d = √( (-5)^2 + (4)^2 )\\\\d = √( 25 + 16 )\\\\d = √( 41 )\\\\`

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A slight alternative is to plot the point M(2,-5) to form right triangle LMN. The 90 degree angle is at point M.

The legs are of length LM = 4 and MN = 5, which are found by subtracting the x coordinates together and the y coordinates together (or you can count the spaces). From there, use the Pythagorean theorem to get the hypotenuse LN.

The distance formula is an altered version of the Pythagorean theorem.