The segment with endpoints A(1,5), and B(1,2) is reflected over x=3, then translated up 2 units and to the right 3 units. We want to find the x-coordinate of the midpoint of the segment after the transformations. We will start with applying the transformations one at a time.
Reflection Over x=3
Let's start with reflecting the segment over x=3. We will plot the segment and show the line of reflection, x=3.
To reflect the segment over x=3, we will reflect the two endpoints and connect them. Move the endpoints to the opposite side of the line of reflection while maintaining the distance of each point from this line.
Using the graph, we can identify the coordinates of the two new endpoints. Note that the y-coordinates did not change.
R_(x=3)(A)=& (5,5)
R_(x=3)(B)=& (4,1)
Therefore, the segment after reflection has the endpoints (5,5), and (4,1).
Translation
Now we will translate the new segment 2 units up and 3 units right. Once again, to do so we need to translate the endpoints 2 units up and 3 units down, then connect them to translate the whole segment. Let's do it!
Midpoint of A'B'
After applying the transformations we have obtained the segment A'B' with endpoints A'(8,7), and B'(7,3). We want to find the x-coordinate of its midpoint. Recall the Midpoint Formula.
(x_1+x_2/2,y_1+y_2/2)
We are only interested in the x-coordinate of the midpoint. In our case x_1= 8 and x_2= 7. We can substitute these values into the formula and simplify.
