Question

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

Answer 1

Answer:   $\sqrt{41}$

On a keyboard you would type sqrt(41)

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Work Shown:

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

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

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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.

Answer 2

Answer:

The distance between the two points provided is: $\sqrt{41}$

Step-by-step 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 = $\sqrt{25+36}$

Second to last, you must add:

d = $\sqrt{41}$

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

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