Respuesta :

Answer:

8 or 32

Step-by-step explanation:

So we are given two coordinates and the length of the segment formed by those coordinates.

To find the unknown coordinate, we can use the distance formula. Let the unknown value be n:

Let's let (-2,n) be x₁ and y₁ and let (-7,20) be x₂ and y₂.

The distance formula is given by the formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute (-2,n) for x₁ and y₁ and (-7,20) for x₂ and y₂. Also, since we already know that the length is 13, substitute it for d. Thus:

[tex](13)=\sqrt{((-7)-(-2))^2+((20)-(n))^2}[/tex]

Do the operations within the parentheses:

[tex]13=\sqrt{(-7+2)^2+(20-n)^2}\\13=\sqrt{(-5)^2+(20-n)^2}[/tex]

Now, square both sides to take out the square root:

[tex](13)^2=(\sqrt{(-5)^2+(20-n)^2})^2[/tex]

Simplify:

[tex]169=(-5)^2+(20-n)^2[/tex]

Square (-5):

[tex]169=25+(20-n)^2[/tex]

Subtract 25 from both sides. The right cancels:

[tex](169)-25=(25+(20-n)^2)-25\\144=(20-n)^2[/tex]

Now, take the square root of both sides.

[tex]\pm\sqrt{144}=\sqrt{(20-n)^2}[/tex]

Simplify:

[tex]\pm12=(20-n)[/tex]

So, we have two solutions:

[tex](12=20-n)\text { or }(-12=20-n)[/tex]

On the left, subtract 20. On the right, also subtract 20:

[tex](-8=-n)\text { or }(-32=-n)[/tex]

Divide both sides by -1:

[tex](n=8)\text{ or } (n=32)[/tex]

So, our two possible answers are 8 or 32.

ACCESS MORE
EDU ACCESS