Question

challenge. the vertices of △abc are a(-4,4), b(-2,3), and c(-1,2). △abc is reflected across the y - axis and then reflected across the x - axis to produce the image △abc. graph △abc and △abc. which graph shows △abc and △abc?

Explanation:

Step1: Recall reflection rules

Reflection across y - axis changes sign of x - coordinate. For point $(x,y)$ it becomes $(-x,y)$. So, $A(-4,4)$ becomes $A'(4,4)$, $B(-2,3)$ becomes $B'(2,3)$ and $C(-1,2)$ becomes $C'(1,2)$.

Step2: Reflect across x - axis

Reflection across x - axis changes sign of y - coordinate. For point $(x,y)$ it becomes $(x, - y)$. So, $A'(4,4)$ becomes $A''(4,-4)$, $B'(2,3)$ becomes $B''(2,-3)$ and $C'(1,2)$ becomes $C''(1,-2)$.

Step3: Analyze graphs

We need to find the graph that has $\triangle ABC$ with vertices $(-4,4),(-2,3),(-1,2)$ and $\triangle A''B''C''$ with vertices $(4,-4),(2,-3),(1,-2)$.

Answer:

(You need to visually check the given graphs to determine which one has the original triangle with the given initial vertices and the final triangle with the calculated vertices after the two - step reflection. Since the actual visual graphs are not described in detail here, the process to find the answer is shown above. You can use the above - calculated coordinates to match the correct graph.)