Question

which single transformation maps △jkl onto its image? choose all that apply. translate 3 units down. translate 7 units down. reflect across the x - axis. reflect across the y - axis. rotate 90° counterclockwise around the origin. rotate 270° counterclockwise around the origin.

Explanation:

Step1: Analyze translation

Translation moves a figure without changing its orientation. By observing the vertical distance between corresponding points of $\triangle{JKL}$ and its image, we can see that it is translated 7 units down. Translating 3 units down is incorrect.

Step2: Analyze reflection

Reflecting across the $x - axis$ would change the sign of the $y -$coordinates of the points. Reflecting across the $y -$axis would change the sign of the $x -$coordinates of the points. Neither of these reflections map $\triangle{JKL}$ to its image.

Step3: Analyze rotation

A $90^{\circ}$ counter - clockwise rotation around the origin changes the coordinates $(x,y)$ to $(-y,x)$. A $270^{\circ}$ counter - clockwise rotation around the origin changes the coordinates $(x,y)$ to $(y, - x)$. These rotations do not map $\triangle{JKL}$ to its image.

Answer:

Translate 7 units down.