Triangle P is reflected in the line $y = -x$ to give triangle Q - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 2

To map triangle R back to triangle P, we first need to analyze the transformations taken to get from P to R.

1. Reflection of Triangle P to Triangle Q: Triangle P was reflected across the line $y = -x$. The reflection changes each point (x, y) of triangle P to the point (-y, -x) for triangle Q.

2. Reflection of Triangle Q to Triangle R: Triangle Q was then reflected across the line $x = 1$. In this case, a point (x, y) of triangle Q will be transformed to the point (2 - x, y) for triangle R, as the reflection line is vertical to the x-axis.

To reverse these transformations and map triangle R back to triangle P, we can apply the inverse of these steps in the reverse order:

3. Reflection of Triangle R Across Line $x = 1$: We first reflect triangle R back across the line $x = 1$. This transforms all points of triangle R to their corresponding points in triangle Q.

4. Reflection of Triangle Q Back Across Line $y = -x$: Finally, we reflect triangle Q across the line $y = -x$ to obtain triangle P again.

In conclusion, the transformation mapping triangle R back to triangle P consists of:

• A reflection of triangle R across the line $x = 1$ followed by
• A reflection of the resulting triangle across the line $y = -x$.