Question

graph the image of \\(\delta jkl\\) after a rotation \\(90^\circ\\) counterclockwise around the origin and a translation 5 units down.

Explanation:

Identify original coordinates

Identify vertices of \(\Delta JKL\):

$$ J = (4, 5),\quad K = (5, 1),\quad L = (1, 1) $$

Apply 90-degree counterclockwise rotation

Using the Coordinate Rotation knowledge point

$$ (x, y) \to (-y, x) $$

$$
LATEXBLOCK0
$$

Apply translation 5 units down

Using the Translation knowledge point

$$ (x, y) \to (x, y - 5) $$

$$
LATEXBLOCK1
$$

Answer:

The coordinates of the vertices of the final image \(\Delta J''K''L''\) are:

$$ J'' = (-5, -1),\quad K'' = (-1, 0),\quad L'' = (-1, -4) $$