Question

kelsey seems to reflect △def across the line y = x. if she drew the image △def, shown below, did kelsey correctly reflect △def across the line y = x? yes, kelsey correctly reflected △def across the line y = x. no, kelsey reflected △def across the y - axis. no, kelsey reflected △def across the x - axis. no, kelsey reflected △def 180° clockwise about the origin.

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the line $y = x$, the new - point is $(y,x)$.

Step2: Check vertices

Check if the vertices of $\triangle DEF$ follow the $(x,y)\to(y,x)$ rule for the transformation to $\triangle D'E'F'$. If not, then the reflection is incorrect. If the coordinates of the vertices of $\triangle DEF$ do not map to the coordinates of the vertices of $\triangle D'E'F'$ according to the $(x,y)\to(y,x)$ rule, we can analyze other transformation rules. Reflection across the $y$ - axis changes $(x,y)$ to $(-x,y)$, reflection across the $x$ - axis changes $(x,y)$ to $(x, - y)$, and a $180^{\circ}$ clock - wise rotation about the origin changes $(x,y)$ to $(-x,-y)$.

Step3: Analyze the graph

By observing the graph, we can see that the transformation from $\triangle DEF$ to $\triangle D'E'F'$ does not follow the $(x,y)\to(y,x)$ rule for reflection across $y = x$. Instead, when we compare the positions of the vertices of $\triangle DEF$ and $\triangle D'E'F'$, we can see that the $x$ - coordinates of the vertices of $\triangle DEF$ have changed their signs while the $y$ - coordinates remain the same. This is the rule for reflection across the $y$ - axis: $(x,y)\to(-x,y)$.

Answer:

No, Kelsey reflected $\triangle DEF$ across the $y$ axis.