Question

Point A is located at (2, 3) on the coordinate plane Point A is reflected over the xaxis to form point B and over the yaxis to form point Thenpoint A reflected over both axes to form point D The four points become vertices of a quadrilateral What is the most precise name for the quadrilateral formedand how do you know?

Answer 1

The quadrilateral formed by reflecting point A (2, 3) over the x and y axes to form points B, C, and D is a rectangle because reflections preserve distances and create parallel lines, resulting in equal and parallel opposite sides and four right angles.

Step-by-step explanation:

When point A with coordinates (2, 3) is reflected over the x-axis, the y-coordinate changes sign, but the x-coordinate remains the same. Therefore, point B would have coordinates (2, -3). Similarly, reflecting point A over the y-axis changes the sign of the x-coordinate, resulting in point C with coordinates (-2, 3). Reflecting over both axes, point D would have coordinates (-2, -3).

The quadrilateral formed by these four points will have equal and parallel opposite sides. This is because reflections over the x and y axes preserve distance and create parallel lines. The most precise name for this quadrilateral is a rectangle, as it has four right angles, and opposite sides are equal and parallel. This classification is confirmed by knowing the original point and applying reflections over the axes.