What are the distances between points and their reflections in horizontal and vertical lines?
a) Which transformation takes ABC to A'B'C?
b) Find the distances between the points. Fill in the table below
c) Compare the vertical distances in adjacent pairs of columns.
What do you notice? Explain.
It is not possible to provide an accurate answer without an accompanying diagram or specified points. Please provide more information.
a) The transformation that takes ABC to A'B'C is a reflection in a vertical line.
b) To find the distances between the points and their reflections in vertical and horizontal lines, we need to know the coordinates of the points and the equations of the reflection lines. Without any specific values, it is not possible to fill in the table.
c) Without the specific values, it is difficult to compare the vertical distances in adjacent pairs of columns. However, when reflecting a point in a vertical line, the x-coordinate remains the same, and only the y-coordinate changes its sign. So if the original point has a positive y-coordinate, its reflection will have a negative y-coordinate, and vice versa.
For example, if we reflect the point (2, 3) in a vertical line, its reflection will be (-2, -3). Therefore, the vertical distance between the point and its reflection would be 6 units.
However, it is important to note that without specific values for the points and reflection lines, it is not possible to make further comparisons and observations about the vertical distances between the points and their reflections.