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

Answer:

Step-by-step 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.