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: 

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.