Question

△lnn is the image of △lmn under a reflection across the y - axis followed by a centered at the origin with scale factor 2. part a graph △lnn in the coordinate plane. part b circle an answer choice in the box to make the statement true. △lnn is ______ to △lmn congruent similar neither congruent nor similar

Explanation:

Part B Solution:

Step1: Recall Transformations

Reflection across the \( y \)-axis is a rigid transformation (preserves shape and size). Dilation with scale factor 2 changes size but preserves shape (angles remain equal, sides are proportional).

Step2: Define Similarity/Congruence

• Congruent: Same shape and size (rigid transformations only: reflection, rotation, translation).
• Similar: Same shape, proportional size (dilation + rigid transformations).

Since dilation (scale factor 2) is applied, the triangles have proportional sides (scale factor 2) and equal angles. Thus, they are similar (not congruent, as size changed).

Answer:

similar

Part A (Graphing) Explanation (Brief):

1. Reflect \(\triangle LMN\) over \( y \)-axis: For a point \((x, y)\), reflection gives \((-x, y)\).
2. Dilate reflected triangle by scale factor 2: Multiply coordinates by 2: \((-x, y) \to (-2x, 2y)\).
3. Plot the new vertices \( L'' \), \( M'' \), \( N'' \) and connect to form \(\triangle L''M''N''\).

(Note: Actual graphing requires original coordinates of \( L, M, N \); assume original coordinates (e.g., \( L(-4,1) \), \( M(-3,3) \), \( N(-1,2) \)):

• Reflect: \( L(4,1) \), \( M(3,3) \), \( N(1,2) \).
• Dilate by 2: \( L''(8,2) \), \( M''(6,6) \), \( N''(2,4) \). Plot these points.)