Please help asap! i need to find the missing coordinate

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:

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:

Do the operations within the parentheses:

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

Simplify:

Square (-5):

Subtract 25 from both sides. The right cancels:

Now, take the square root of both sides.

Simplify:

So, we have two solutions:

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

Divide both sides by -1:

So, our two possible answers are 8 or 32.