Question

1. perform the following glide reflection on point j with coordinates (3, -5).

translation: (x, y) → (x - 4, y + 3)
reflection: in the y - axis.
j=(3, -5) j=__ j=__
vocabulary - match the vocabulary term to its description.

1. ____a function that moves or changes a figure in some way to produce a new figure (including translations, reflections, rotations and dilations).
2. ____the original figure as it exists before undergoing a transformation.
3. ____another name for the figure after undergoing a transformation.
4. ____a type of transformation in which a figure simply moves left, right, up, or down.
5. ____a type of transformation that uses a line like a mirror to reflect a figure.
6. ____a type of transformation in which a figure is turned about a fixed point called the center of rotation.
7. write a sentence describing the transformation rule: (x, y) → (x - 7, y +
8. what type of transformation moves a figure left, right, up or down?
9. pont x(-3, -2) is translated using the rule (x, y) -> (x + 3, y + 5), then reflected over the x - axis. what are the coordinates of x?
10. describe in your own words what happens to the x & y coordinates when you rotate them

90° counterclockwise?
b). rotate them 180 degrees?

Explanation:

Step1: Find \(J'\) using translation

Given the translation rule \((x,y)\to(x - 4,y + 3)\) and \(J=(3,-5)\).
For the \(x\) - coordinate: \(x'=3-4=-1\).
For the \(y\) - coordinate: \(y'=-5 + 3=-2\).
So, \(J'=(-1,-2)\).

Step2: Find \(J''\) using reflection

The reflection rule over the \(y\) - axis is \((x,y)\to(-x,y)\).
Since \(J'=(-1,-2)\), for the \(x\) - coordinate: \(x''=-(-1) = 1\), and the \(y\) - coordinate remains \(y''=-2\).

Answer:

\(J'=(-1,-2)\), \(J''=(1,-2)\)