Shape A can be transformed to shape B by a reflection in the x-axis followed by a translation Find the value of c and the value of d. - Edexcel - GCSE Maths - Question 6 - 2019 - Paper 1

Reflection in the x-axis: The reflection of shape A in the x-axis involves changing the y-coordinates of the vertices of shape A. For instance, if the coordinates of shape A are given as (x, y), after reflection, it becomes (x, -y).

Identifying vertices: Let’s denote the vertices of shape A as A(2, 3) and B(0, 1). After reflecting these points in the x-axis, their new coordinates will be A'(2, -3) and B'(0, -1).

Translation to shape B: Now that we have the coordinates of shape A after reflection, we compare these with the coordinates of shape B. Let’s assume the coordinates of shape B to be (x', y'). Assuming the vertex in shape B that corresponds to A' is B'(0, -3), we need to calculate the translation values c and d.

Finding c and d: By applying the transformation of the form (x, y) → (x + c, y + d), if we see that:

• For x-coordinates: We observe that 2 + c = 0 Hence, $c = -2$
• For y-coordinates: As the original y-coordinate transformed from -3 to -7, we have: $-3 + d = -7$
  Thus, $d = -4$

Final results: The values of c and d are:

• c = -2
• d = -4