Question

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

Explanation:

Identify original coordinates

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

Apply reflection over the x-axis

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

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

Apply translation 4 units right

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

$$ A'' = (-5 + 4, -3) = (-1, -3) $$

$$ B'' = (-2 + 4, -1) = (2, -1) $$

$$ C'' = (-5 + 4, -1) = (-1, -1) $$

Answer:

The coordinates of the image \(\Delta A''B''C''\) after a reflection over the \(x\)-axis and a translation 4 units right are:

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