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.