Question

Quadrilateral ABCD with vertices A(-9,2) , B(-8,8) C(-4,6) and D(-2,2) is shown. You want to reflect quadrilateral ABCD in the vertical line that passes through the the midpoint of side BC. Graph the line of reflection and the image after the reflection.

Answer 1

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.