Question

A rectangle is plotted on a coordinate plane with corners at M(0, 0), N(0, 4), O(5, 4), and P(5, 0). This rectangle is reflected across the x-axis and then translated 2 units to the left to form figure M'N'O'P'.

Drag each line segment on the left to the appropriate group on the right.

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Answers

Line segments parallel to

Line segments parallel to

Answer 1

To categorize the line segments of the rectangle M(0, 0), N(0, 4), O(5, 4), and P(5, 0) and their reflected and translated shape M'N'O'P', we should first identify the line segments in the original rectangle and their respective orientations.

**Original Rectangle Corners:**
- M(0, 0)
- N(0, 4)
- O(5, 4)
- P(5, 0)

**Line Segments in the Original Rectangle:**
1. MN (vertical line segment) between M(0, 0) and N(0, 4)
2. NO (horizontal line segment) between N(0, 4) and O(5, 4)
3. OP (vertical line segment) between O(5, 4) and P(5, 0)
4. PM (horizontal line segment) between P(5, 0) and M(0, 0)

**Reflection Across the x-axis:**
When the rectangle is reflected across the x-axis, the new coordinates are:
- M'(0, 0)
- N'(0, -4)
- O'(5, -4)
- P'(5, 0)

**Translation 2 Units to the Left:**
After translating each point 2 units to the left, the coordinates become:
- M'(-2, 0)
- N'(-2, -4)
- O'(3, -4)
- P'(3, 0)

**Line Segments in the Transformed Rectangle (after Reflection and Translation):**
1. M'N' (vertical line segment) between M'(-2, 0) and N'(-2, -4)
2. N'O' (horizontal line segment) between N'(-2, -4) and O'(3, -4)
3. O'P' (vertical line segment) between O'(3, -4) and P'(3, 0)
4. P'M' (horizontal line segment) between P'(3, 0) and M'(-2, 0)

**Grouping by Parallel Line Segments:**

**Line segments parallel to the y-axis:**
- MN (original)
- OP (original)
- M'N' (reflected and translated)
- O'P' (reflected and translated)

**Line segments parallel to the x-axis:**
- NO (original)
- PM (original)
- N'O' (reflected and translated)
- P'M' (reflected and translated)

**Final Grouping:**
- **Line segments parallel to the y-axis:**
- MN, OP, M'N', O'P'

- **Line segments parallel to the x-axis:**
- NO, PM, N'O', P'M'

You should drag the line segments accordingly to form these groups.