Question

1. triangle abc is graphed on a coordinate grid so that a is (5,7), b is (0,-3) and c is (-3,9). the triangle is reflected across the y - axis to create triangle xby where angle a corresponds to angle x. which side corresponds to side ac? options: xy, xb, yb, ax

Explanation:

To determine the corresponding side to \( AC \) after reflecting \( \triangle ABC \) across the \( y \)-axis:

1. Recall the reflection rule over the \( y \)-axis: \((x,y) \to (-x,y)\).
2. Find the coordinates of the reflected points:

• For \( A(5,7) \), the reflection \( X \) is \((-5,7)\) (since angle \( A \) corresponds to angle \( X \)).
• For \( C(-3,9) \), the reflection \( Y \) is \((3,9)\) (since \( C \) should correspond to \( Y \) as \( A \) corresponds to \( X \) and \( B \) is on the \( y \)-axis, so \( B(0,-3) \) reflects to itself).

1. Analyze the sides:

• Side \( AC \) in \( \triangle ABC \) connects \( A(5,7) \) and \( C(-3,9) \).
• After reflection, the corresponding side should connect \( X(-5,7) \) (reflection of \( A \)) and \( Y(3,9) \) (reflection of \( C \)). Wait, but looking at the options, we re - evaluate the correspondence:
• Since \( B \) is on the \( y \)-axis, \( B \) reflects to \( B \) itself. The correspondence of vertices is \( A \to X \), \( B \to B \), \( C \to Y \).
• So side \( AC \) (connecting \( A \) and \( C \)) should correspond to side \( XY \) (connecting \( X \) (reflection of \( A \)) and \( Y \) (reflection of \( C \))).

Answer:

A. \( XY \)