What are the coordinates of two pairs of points for the other vertices on a square?

Question

This problem is one that I have in my geometry book, and the book and my answers disagree.

Two vertices of a square are (3, -2) and (3, 6). What are the coordinates of two pairs of points for the other vertices? a. ________ b. _________

The book says that the other points are (11, 6) and (11, -2). The ones that I believe are correct are (-5, -6) and (-5, -2)

Answer 1

(-5, -6) and (-5, -2) are not correct: Plotting the points (3, -2), (3, 6), (-5, -6), and (-5, -2) gives the following configuration:

However, both ((-5, 6), (-5, -2)) and ((11, 6), (11, -2)) are correct solutions: the first pair of points lies 8 units to the left of the points ((3, 6), (3, -2)), and the other pair lies 8 units to the right.

Answer 2

I recently learned complex numbers and I think I can use them now. Here's my solution..sorry I didn't use MathJax coz I'm a newbie.

(https://i.stack.imgur.com/RwVgX.jpg)

So yes I guess (-5,6) and (-5,-2) are correct.

Answer 3

Increments of square dimension are noted in $y$ direction

The square has a side length $ 6-(-2)= 8$

Add that to x- coord

$$ (3+8, -2 ), (3+8,6)\implies (11,-2), (11,6) $$

Subtract that from the x- coord

$$ (3-8, -2 ), (3-8,6) \implies (-5,-2), (-5,6). $$

There are two options and both are correct.