Question

what is the mapping for the reflection where $\triangle abc$ maps to $\triangle abc$?
options:
$\boldsymbol{(x,y) \to (x, -y)}$
$\boldsymbol{(x,y) \to (-x, y)}$
$\boldsymbol{(x,y) \to (x, y)}$
$\boldsymbol{(x,y) \to \left(x, -\frac{1}{2}y\
ight)}$
question 5
1 pts
which of the following is the correct mapping for shape a to shape b?

Explanation:

Step1: Analyze Coordinates

Let's take point \( A \). Suppose \( A \) has coordinates \( (x, y) \). From the graph, \( A \) is above the \( x \)-axis, and \( A' \) is below, with the same \( x \)-coordinate. Similarly for \( B \) and \( B' \), \( C \) and \( C' \).

Step2: Identify Reflection Rule

Reflection over the \( x \)-axis has the mapping \( (x, y) \to (x, -y) \), which matches the transformation here (since \( y \)-coordinate is negated, \( x \)-coordinate stays same). Other options: \( (-x, y) \) is reflection over \( y \)-axis, \( (x, y) \) is no change, \( (x, -\frac{1}{2}y) \) is a vertical stretch/compression, not reflection.

Answer:

\( (x, y) \to (x, -y) \)