Question

try it! graph each transformation and label its vertices. the first problem has been done for you.
graph the image of △... rotation 90° counterclockwise and a reflection over the y - axis
graph the image of △abc after a reflection over the x - axis and a translation 4 units right.
graph the image of △jkl after a rotation 90° counterclockwise around the origin and a translation 5 units down.
graph the image of trapezoid tuvw after a translation 2 units left and a reflection over the y - axis.
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Explanation:

Step1: Identify Vertices of ΔJKL

First, find the coordinates of vertices \( J \), \( K \), and \( L \) from the graph. From the grid:

• \( L \): \( (1, 1) \)
• \( K \): \( (5, 1) \)
• \( J \): \( (4, 5) \)

Step2: Apply 90° Counterclockwise Rotation

The rule for a 90° counterclockwise rotation about the origin is \( (x, y) \to (-y, x) \).

• For \( L(1, 1) \): \( (1, 1) \to (-1, 1) \)
• For \( K(5, 1) \): \( (5, 1) \to (-1, 5) \)
• For \( J(4, 5) \): \( (4, 5) \to (-5, 4) \)

Step3: Apply Translation 5 Units Down

The rule for translating 5 units down is \( (x, y) \to (x, y - 5) \).

• For rotated \( L(-1, 1) \): \( (-1, 1 - 5) = (-1, -4) \)
• For rotated \( K(-1, 5) \): \( (-1, 5 - 5) = (-1, 0) \)
• For rotated \( J(-5, 4) \): \( (-5, 4 - 5) = (-5, -1) \)

Step4: Graph the Transformed Vertices

Plot the points \( (-1, -4) \), \( (-1, 0) \), and \( (-5, -1) \) on the coordinate plane and connect them to form the image of \( \triangle JKL \) after the transformations.

Answer:

The image of \( \triangle JKL \) after a 90° counterclockwise rotation about the origin and a translation 5 units down has vertices at \( (-1, -4) \), \( (-1, 0) \), and \( (-5, -1) \) (graph these points to see the transformed triangle).