Question

choose all that apply ( multiple solutions)
triangle abc and triangle ade are shown.
select all of the transformations that could be performed to carry triangle abc onto triangle ade.
a a reflection across the line y = -x
b a reflection across the x - axis, and then a reflection across the y - axis
c a rotation of 90 degrees clockwise about the origin, and then a reflection across the y - axis
d a rotation of 90 degrees clockwise about the origin, and then a reflection across the x - axis
e a rotation of 180 degrees clockwise about the origin, and then a reflection across the line y = -x

Explanation:

Step1: Recall transformation rules

Understand rules for reflection and rotation.

Step2: Analyze option A

Reflection across $y = -x$ swaps $(x,y)$ to $(-y,-x)$. Analyze if it maps $\triangle ABC$ to $\triangle ADE$.

Step3: Analyze option B

Reflection across $x$ - axis changes $(x,y)$ to $(x, - y)$, then reflection across $y$ - axis changes $(x,-y)$ to $(-x,-y)$. Check the mapping.

Step4: Analyze option C

$90$ - degree clockwise rotation about origin changes $(x,y)$ to $(y,-x)$, then reflection across $y$ - axis changes $(y,-x)$ to $(-y,-x)$. See if it works.

Step5: Analyze option D

$90$ - degree clockwise rotation about origin gives $(y,-x)$, then reflection across $x$ - axis gives $(y,x)$. Check the mapping.

Step6: Analyze option E

$180$ - degree clockwise rotation about origin changes $(x,y)$ to $(-x,-y)$, then reflection across $y=-x$ swaps $(-x,-y)$ to $(y,x)$. Check the mapping.

Answer:

A. a reflection across the line $y=-x$
B. a reflection across the $x$-axis, and then a reflection across the $y$-axis
E. a rotation of 180 degrees clockwise about the origin, and then a reflection across the line $y = -x$