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Draw a figure of quadrilateral ABCD having the vertices A(4, 8) B(6, 6) , C(4,4) and D(3,6) on the graph. It is reflected on the line Y = 4 and draw A' * B' * C' * D' . Then, reflect it on the line y=0 and drawA"*B"*C"*D" on the same graph and find the coordinates of A",B",C"andD". what single transformation does these two reflection represent​



Answer :

To solve this problem, we need to follow these steps:

Step 1: Draw the quadrilateral ABCD on the graph with the given vertices.

Step 2: Reflect the quadrilateral ABCD on the line y = 4 to obtain A'B'C'D'.

Step 3: Reflect the quadrilateral A'B'C'D' on the line y = 0 to obtain A"B"C"D".

Step 4: Find the coordinates of A", B", C", and D".

Step 5: Identify the single transformation that these two reflections represent.

Here's the step-by-step solution with the figure:

```
y
10 |
9 |
8 | A(4,8)
7 |
6 | B(6,6) D(3,6)
5 |
4 |-----------------------------
3 | C'(4,4) B'(6,2)
2 | A'(4,0) D'(3,2)
1 |
0 |-----------------------------
-1 | A"(4,0) D"(3,-2)
-2 | C"(4,-4) B"(6,-2)
-3 |
+-----------------------------
0 1 2 3 4 5 6 7 8
```

The coordinates of the vertices after the two reflections are:
A" = (4, 0)
B" = (6, -2)
C" = (4, -4)
D" = (3, -2)

These two reflections (reflection on y = 4 and then reflection on y = 0) represent a single transformation called a rotation of 180 degrees about the origin (0, 0).

Therefore, the single transformation that these two reflections represent is a rotation of 180 degrees about the origin.

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