Question

suppose the equation of line (l) is (y = x). which shows the graph of (\triangle abc) for (r_{l})?

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the line $y = x$, the transformation rule is $(x,y)\to(y,x)$.

Step2: Assume coordinates of $\triangle ABC$

Let's assume $A=(0, 2)$, $B=(2,0)$, $C=(- 2,0)$.

Step3: Apply reflection rule to points

For point $A(0,2)$, after reflection over $y = x$, $A'\to(2,0)$. For point $B(2,0)$, $B'\to(0,2)$. For point $C(-2,0)$, $C'\to(0, - 2)$.

Answer:

We need to check which of the given graphs (not fully - shown here but based on the above - calculated coordinates of the reflected points) has the correct positions of $A'$, $B'$ and $C'$. If we assume the standard coordinate - based reflection as calculated above, we can match the graph accordingly. Without seeing all the options, we know that the vertices of the reflected triangle will have their $x$ and $y$ coordinates swapped compared to the original triangle's vertices.