Question

triangle abc is reflected over the line y = x to produce triangle abc. what will be the coordinates of a? a. (2, -1) b. (-2, -1)

Explanation:

Step1: Recall reflection rule

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

Step2: Identify coordinates of A

The coordinates of point A are $(2,1)$.

Step3: Apply reflection rule

Using the rule $(x,y)\to(y,x)$ for point A$(2,1)$, we get $(1,2)$. But there is no such option. Let's double - check the rule application. When reflecting $(x,y)$ over $y = x$, we swap the $x$ and $y$ values. For point A with coordinates $(2,1)$, after reflection over $y=x$, the new coordinates of $A'$ are $(1,2)$. Since this is not in the options, we assume there is a mis - typing in the options or in our understanding. Re - applying the rule correctly, for a point $(x,y)$ reflected over $y = x$, the image has coordinates $(y,x)$. Given $A=(2,1)$, $A'=(1,2)$. Since it's not in the options, we note the correct transformation concept. If we consider the general rule of reflection over $y = x$: If $A=(x_1,y_1)=(2,1)$, then $A'=(y_1,x_1)=(1,2)$. But if we assume the question setter might have made a mistake and we consider the closest correct concept application among the options, when reflecting a point $(x,y)$ over $y = x$, we swap the $x$ and $y$ values.

Answer:

None of the given options are correct. The correct coordinates of $A'$ after reflecting point $A(2,1)$ over the line $y = x$ should be $(1,2)$.