A reflection across the x-axis followed by a translation [math]\left(\begin{matrix}3\\0\end{matrix}\right)[/math].
Part 2: Find the Image Coordinates
Move triangle XYZ with vertices X(0, 0), Y(2, 4), Z(4, 0) by the vector [math]\left(-3,2\right)[/math]
X'(-3, 2), Y'(-1, 6), Z'(1, 2)
Reflect L(1, 5) and M(4, 8) across the line [math]y=x[/math].
L'(5, 1), M'(8, 4)
Rotate A(2, 6) [math]90^o[/math] counter-clockwise about the origin.
A'(-6, 2)
Reflect B(2, 3) across the x-axis, then translate it by [math]\left(\begin{matrix}4\\0\end{matrix}\right)[/math].
B'(6, -3)
Part 3: Critical Thinking
If a triangle is reflected across the y-axis and then reflected again across the x-axis, which single isometry would produce the same result?
A [math]180^\circ[/math] rotation about the origin.
A shape is translated 2 units right and 2 units up, then reflected across the line y = x. Is the resulting transformation a Glide Reflection? Explain why or why not.
Yes, it is a glide reflection. A glide reflection requires the translation vector to be parallel to the line of reflection.