Photo AI
The diagram shows a triangle P on a grid - Edexcel - GCSE Maths - Question 12 - 2020 - Paper 3
Question 12
The diagram shows a triangle P on a grid. Triangle P is rotated 180° about (0, 0) to give triangle Q. Triangle Q is translated by (−5, 2) to give triangle R. (a) D... show full transcript
Worked Solution & Example Answer:The diagram shows a triangle P on a grid - Edexcel - GCSE Maths - Question 12 - 2020 - Paper 3
Step 1
Describe fully the single transformation that maps triangle P onto triangle R.
Answer
To map triangle P onto triangle R, we can break down the transformations into two distinct parts:
-
Rotation of Triangle P: Triangle P is rotated 180° about the origin (0, 0). This rotation changes the coordinates of each vertex of triangle P by the following rule:
- If a point has coordinates (x, y), after a 180° rotation about the origin, the new coordinates will be (-x, -y).
-
Translation of Triangle Q: After obtaining triangle Q from the rotation, we then translate it by the vector (−5, 2). This means that we subtract 5 from the x-coordinates and add 2 to the y-coordinates of each vertex of triangle Q.
In summary, the complete transformation from triangle P to triangle R consists of a 180° rotation followed by a translation of (−5, 2).
Step 2
Write down the coordinates of point A.
Answer
To find the coordinates of point A after the transformations:
- Original Coordinates of A: Let's assume point A has coordinates (x_A, y_A) in triangle P.
- Apply the Rotation: After a 180° rotation, the new coordinates become (-x_A, -y_A).
- Apply the Translation: Next, we translate these coordinates by adding (−5, 2).
Therefore, the final coordinates of point A are:
If we assume A was at (2, -1) in triangle P, the calculations would be:
- Rotation gives (-2, 1).
- Translation yields (-2 - 5, 1 + 2) = (-7, 3).
Thus, the coordinates of point A after the transformations are (-7, 3).