Question

graph the image of \\(\delta abc\\) after a reflection over the x-axis and a translation 4 units right.

Explanation:

Identify original coordinates

Identify the coordinates of the vertices of \(\triangle ABC\) from the graph:

$$ A(-5, 3), \quad B(-2, 1), \quad C(-5, 1) $$

Apply reflection over the x-axis

Using the Reflection knowledge point

$$ (x, y) ightarrow (x, -y) $$

$$
LATEXBLOCK0
$$

Apply translation 4 units right

Using the Translation knowledge point

$$ (x, y) ightarrow (x + 4, y) $$

$$
LATEXBLOCK1
$$

Verify final coordinates

Using the Geometric Transformations knowledge point

$$
LATEXBLOCK2
$$

Answer:

The coordinates of the vertices of the image \(\triangle A''B''C''\) after a reflection over the \(x\)-axis followed by a translation 4 units to the right are:

• \(A''(-1, -3)\)
• \(B''(2, -1)\)
• \(C''(-1, -1)\)