Photo AI
Triangles A and B are drawn on the coordinate grid - OCR - GCSE Maths - Question 11 - 2019 - Paper 1
Question 11
Triangles A and B are drawn on the coordinate grid. (a) Describe fully the single transformation that maps triangle A onto triangle B. (b) (i) On the grid, reflect... show full transcript
Worked Solution & Example Answer:Triangles A and B are drawn on the coordinate grid - OCR - GCSE Maths - Question 11 - 2019 - Paper 1
Step 1
Describe fully the single transformation that maps triangle A onto triangle B.
Answer
The transformation that maps triangle A onto triangle B is a reflection across the x-axis. To describe it fully, we see that triangle B is the mirror image of triangle A with respect to the x-axis. Thus, a reflection over the x-axis appropriately describes the mapping of triangle A to triangle B.
Step 2
(i) On the grid, reflect triangle A in the line x = 0. Label the image C.
Answer
To reflect triangle A in the line , we will switch the signs of the x-coordinates of each vertex of triangle A. The coordinates of triangle A before reflection will be (for example) (x1, y1), (x2, y2), (x3, y3), making the reflected coordinates (for image C) as follows:
- (x1, y1) becomes (-x1, y1)
- (x2, y2) becomes (-x2, y2)
- (x3, y3) becomes (-x3, y3)
Label this reflected triangle as C.
Step 3
(ii) On the grid, translate triangle A by vector \begin{pmatrix}-5\\ -4\end{pmatrix}. Label the image D.
Answer
To translate triangle A by the vector , we will subtract 5 from the x-coordinates and subtract 4 from the y-coordinates of each vertex of triangle A. Assuming the vertices of triangle A are at (x1, y1), (x2, y2), (x3, y3), the new vertices for image D will be:
- (x1 - 5, y1 - 4)
- (x2 - 5, y2 - 4)
- (x3 - 5, y3 - 4)
Label this translated triangle as D.