Question

which graph shows ( \triangle abc ) and its reflection across the ( y )-axis, ( \triangle abc )?

choose the correct answer below:

( \bigcirc ) a.
graph of a triangle and another triangle below it

( \bigcirc ) b.
graph of a triangle and its reflection across the ( y )-axis

( \bigcirc ) c.
graph of a triangle and another triangle to the right

Explanation:

To determine the correct graph for the reflection of \(\triangle ABC\) across the \(y\)-axis, we use the rule for reflecting a point \((x, y)\) across the \(y\)-axis: the \(x\)-coordinate changes sign, while the \(y\)-coordinate remains the same, i.e., \((x, y) \to (-x, y)\).

Step 1: Analyze Option A

In Option A, the triangles appear to be reflected across the \(x\)-axis (since the \(y\)-coordinates change sign) rather than the \(y\)-axis. So, this is incorrect.

Step 2: Analyze Option B

In Option B, the triangles are symmetric with respect to the \(y\)-axis. For each point in \(\triangle ABC\), its reflection across the \(y\)-axis (changing the \(x\)-coordinate's sign) gives the corresponding point in \(\triangle A'B'C'\). This follows the reflection rule.

Step 3: Analyze Option C

In Option C, the triangles seem to be translated horizontally rather than reflected across the \(y\)-axis. The symmetry with respect to the \(y\)-axis is not present here. So, this is incorrect.

Answer:

B