Question

Quadrilateral PQRS is mapped onto its image using which of the following sets of transformations?

Answer 1

Reflection across x = -2; clockwise rotation of 90° about the origin

Explanation:

Answer 2

Reflection across x = -2; clockwise rotation of 90° about the origin

Explanation:

Assume that the mapping is like that in Fig. 1.

1. Reflection about x = -2

It looks like the first transformation is a reflection about the line x = -2

When you reflect a shape about a line, each point in the image is the same distance from the line of reflection as the corresponding point in the pre-image.

The rule for reflection about a line x = h is (x,y) ⟶ (2h - x, y}

We can use the rule to calculate the coordinates of the first image.

`\begin{array}{cc}\textbf{A} & \textbf{A`

2. Rotation 90° clockwise about the origin

It looks like the second transformation is a 90° clockwise rotation about the origin.

The rule is (x,y) ⟶ (y,-x).

In other words, interchange x and y and make x negative.

`\begin{array}{cc}\textbf{A`

These are the coordinates of P'Q'R'S'.

Figure 2 shows the reflection of A across the line x = -2 to give A" and its rotation to give A'.