Reflection
We are given a figure with a quadrilateral with known vertices at A(-9,2), B(-8,8) C(-4,6), and D(-2,2).
We'll label the vertices in the figure below:
The quadrilateral is to be reflected about the vertical line that passes through E(-6, 7), the midpoint of BC. The result is shown below:
Now, to reflect each point about this line, we map them to another point that has the same y-coordinate and has a new x-coordinate that is located at the same distance from the reflection line.
For example, point B(-8, 8) is at a distance of -6 + 8 = 2 units from the line. So the new x-coordinate must be 2 units to the right of the line, that is at x = -4. This means that point B(-8, 8) maps to B'(-4, 8).
Following the same procedure:
Point C(-4, 6) maps to C'(-8, 6)
Point A(-9, 2) maps to A'(-3, 2)
Point D(-2, 2) maps to D'(-10, 2)
In the next figure, we'll show the reflected quadrilateral along with the original quadrilateral.
