Question

1. graph & label the images of the sequence of transformations.

reflect \\(\delta xyz\\) over the y-axis
rotate \\(\delta xyz\\) \\(90^\circ\\)

Explanation:

Identify the original coordinates

Identify the coordinates of the vertices of \(\Delta XYZ\) from the given coordinate grid:

$$ X(-2, -4), \quad Y(-7, -1), \quad Z(-5, -4) $$

Reflect over the y-axis

Using the Reflection and Geometric Transformations knowledge points

$$
LATEXBLOCK0
$$

Rotate 90 degrees counterclockwise

Apply a standard counterclockwise rotation of \(90^\circ\) about the origin:

$$
LATEXBLOCK1
$$

Answer:

The coordinates of the vertices after the sequence of transformations are:

Original Triangle \(\Delta XYZ\):

• \(X(-2, -4)\)
• \(Y(-7, -1)\)
• \(Z(-5, -4)\)

After Reflection over the y-axis (\(\Delta X'Y'Z'\)):

• \(X'(2, -4)\)
• \(Y'(7, -1)\)
• \(Z'(5, -4)\)

After \(90^\circ\) Counterclockwise Rotation (\(\Delta X''Y''Z''\)):

• \(X''(4, 2)\)
• \(Y''(1, 7)\)
• \(Z''(4, 5)\)