Question

graph the image of \\(\delta fgh\\) after a rotation \\(90^\circ\\) counterclockwise around the origin and a reflection over the \\(y\\)-axis.

Explanation:

Identify the coordinates of the original vertices

The original triangle \(\Delta FGH\) has the following vertices:

$$ F(2, -2),\quad G(4, -6),\quad H(1, -6) $$

Apply a \(90^\circ\) counterclockwise rotation around the origin

The coordinate rule for a \(90^\circ\) counterclockwise rotation is \((x, y)
ightarrow (-y, x)\):

$$
LATEXBLOCK0
$$

Apply a reflection over the y-axis

The coordinate rule for a reflection over the y-axis is \((x, y)
ightarrow (-x, y)\):

$$
LATEXBLOCK1
$$

Answer:

The coordinates of the final image \(\Delta F''G''H''\) after a \(90^\circ\) counterclockwise rotation around the origin followed by a reflection over the y-axis are:

$$ F''(-2, 2),\quad G''(-6, 4),\quad H''(-6, 1) $$