### Instruction: The point $A$ $(3,4)$ is reflected over the $x$-axis to $B$. Then $B$ is reflected over the line $y=x$ to $C$. What is the area of triangle $ABC$?### Response: To find the area of a triangle, I need to know its base and height, or use a formula involving its coordinates.
I can easily find the coordinates of $B$ by reflecting $A$ over the $x$-axis.
That means changing the sign of the $y$-coordinate, so $B$ is $(3,-4)$.
To find the coordinates of $C$, I need to reflect $B$ over the line $y=x$.
That means swapping the $x$ and $y$ coordinates, so $C$ is $(-4,3)$.
Now I have the coordinates of all three vertices of the triangle.