Question

which triangle shows the final image? (image of coordinate grid with triangles abc and labeled triangles 1, 2, 3, 4)

Explanation:

To solve this, we analyze the transformation of \(\triangle ABC\):

Step 1: Identify \(\triangle ABC\)’s orientation

\(\triangle ABC\) is a right triangle with the right angle at \(B\), and the legs (vertical and horizontal) are aligned with the grid. The “height” (vertical leg) and “base” (horizontal leg) are positive (assuming standard grid directions).

Step 2: Analyze transformations (translation, reflection, rotation)

We compare \(\triangle ABC\) to triangles 1–4:

• Triangle 4: Matches the orientation, size, and position after the intended transformation (likely translation or rotation/reflection that preserves the right - angled, leg - aligned structure of \(\triangle ABC\)). Other triangles (1, 2, 3) have incorrect orientations (e.g., flipped or rotated in a way that misaligns the legs or changes the right - angle position) or sizes.

Step1: Analyze \(\triangle ABC\)’s shape

\(\triangle ABC\) is a right triangle with legs along grid lines (right angle at \(B\)).

Step2: Compare with options

Triangle 4 has the same orientation, leg alignment, and size as \(\triangle ABC\) after transformation. Other triangles (1, 2, 3) have incorrect orientations/sizes.

Answer:

4 (the triangle labeled 4)