Question

$\triangle abc$ has vertices $a(3, -5)$, $b(1, -4)$, and $c(4, -2)$. which graph shows the image of $\triangle abc$ after a reflection in the $y$-axis, followed by a rotation of $270^\circ$ counterclockwise about the origin?

Explanation:

Step1: Reflect points over y-axis

For a point $(x,y)$, reflection over y-axis is $(-x,y)$.

• $A(3,-5) \to A'(-3,-5)$
• $B(1,-4) \to B'(-1,-4)$
• $C(4,-2) \to C'(-4,-2)$

Step2: Rotate 270° counterclockwise about origin

The rule for 270° counterclockwise rotation about origin is $(x,y) \to (y,-x)$.

• $A'(-3,-5) \to A''(-5, 3)$
• $B'(-1,-4) \to B''(-4, 1)$
• $C'(-4,-2) \to C''(-2, 4)$

Step3: Match to the graph

Plot $A''(-5, 3)$, $B''(-4, 1)$, $C''(-2, 4)$ and compare to the options.

Answer:

D. The graph with points $A''$ in the lower left, $B''$ near the lower middle, and $C''$ in the upper left of the grid