Question

If the points at (-4, 3) and (2, 3) are reflected over the x-axis to create two new points, what shape can be formed by the four points? Select the most precise description of the shape.

Answer 1

I have no idea what the other person said, but the answer is square if you want a simple answer.

Answer 2

Explanation:

Let
`(a,b)\in \mathbb{R}^(2)`, a reflection over the x-axis consists in the following operation:

`(a,b) \rightarrow (a,-b)`

If we know that
`X = (-4,3)` and
`Y = (2, 3)`, then the points translated over the x-axis are
`X' = (-4, -3)` and
`Y' = (2,-3)`, respectively. The most precise description of the shape is a rectangle for the following facts:

1)
`XX' = YY' = 8` and
`XY = X'Y' = 6`.

2)
`X` and
`X'` have the same x-component.

3)
`Y` and
`Y'` have the same x-component.

4)
`X` and
`Y` have the same y-component.

5)
`X'` and
`Y'` have the same y-component.

A representation of the shape is included below as attachment.