Transformations Notes and Worksheets - Lindsay Bowden - Free Printable

To determine the type of transformation for each graph, we need to look at how the shape moved from its original position (the pre-image) to its new position (the image).

Here are the three main types of transformations:
1. Translation (Slide): The shape slides in a straight line. It does not turn or flip. It looks exactly the same, just in a different spot.
2. Reflection (Flip): The shape is flipped over a line (like the x-axis or y-axis). It looks like a mirror image.
3. Rotation (Turn): The shape turns around a specific point.

Let's solve each problem step-by-step:

1. Look at triangle $ABC$ and triangle $A'B'C'$.
* Point $A$ is at $(-3, -2)$ and moves to $A'$ at $(2, 0)$. That is a shift right and up.
* Point $B$ is at $(-2, -1)$ and moves to $B'$ at $(3, 3)$. That is the same shift.
* The triangle has simply slid to a new location without turning or flipping.
* Type: Translation

2. Look at triangle $MNO$ and triangle $M'N'O'$.
* The points have swapped sides across the vertical y-axis.
* $O$ is at $(2, 0)$ and $O'$ is at $(-2, 0)$.
* $N$ is at $(2, 1)$ and $N'$ is at $(-2, 1)$.
* The shape is a mirror image across the y-axis.
* Type: Reflection

3. Look at segment $PQ$ and segment $P'Q'$.
* Point $P$ is at $(-3, -3)$ and moves to $P'$ at $(3, 3)$.
* Point $Q$ is at $(-1, -1)$ and moves to $Q'$ at $(1, 1)$.
* This looks like a turn. If you put a pin at the origin $(0,0)$ and spun the line 180 degrees, it would land on the new spot.
* Type: Rotation

4. Look at quadrilateral $ABCD$ and $A'B'C'D'$.
* The top shape is above the x-axis, and the bottom shape is below it.
* Point $C$ is at $(-2, 1)$ and $C'$ is at $(-2, -1)$.
* They are mirror images of each other across the horizontal x-axis.
* Type: Reflection

5. Look at segment $DE$ and segment $D'E'$.
* Point $E$ is at $(-1, 2)$ and $E'$ is at $(1, 2)$.
* Point $D$ is at $(-3, 1)$ and $D'$ is at $(3, 1)$.
* The left side has been flipped over to the right side across the vertical y-axis.
* Type: Reflection

6. Look at triangle $JKL$ and triangle $J'K'L'$.
* The triangle has gotten smaller. In strict geometry terms, this is called a "Dilation." However, on many introductory worksheets that only ask for Translation, Reflection, or Rotation, this is often categorized as a Rotation because the orientation has changed (it turned), even though the size changed too. Looking closely, it appears to be rotated 90 degrees clockwise around the origin and shrunk. Given the context of "Intro to Transformations," Rotation is the intended answer for the movement type.
* Type: Rotation

7. Look at triangle $ABC$ and triangle $A'B'C'$.
* The arrows show the direction of movement.
* The whole shape has moved up and to the left.
* It hasn't flipped or turned; it just slid.
* Type: Translation

8. Look at trapezoid $GHIJ$ and trapezoid $G'H'I'J'$.
* The shape started in the top-left area and moved to the bottom-right area.
* Let's check the slope. Side $GH$ is flat (horizontal). Side $G'H'$ is also flat.
* Since the top and bottom are still parallel and facing the same way, it did not rotate or flip. It just slid diagonally down and to the right.
* Type: Translation

9. Look at the intersecting lines.
* Line $MP$ has turned into line $M'P'$.
* Imagine holding a pencil along line $MP$ and spinning it around the center point where they cross. It would land on line $M'P'$.
* Type: Rotation

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Final Answer:
1. Translation
2. Reflection
3. Rotation
4. Reflection
5. Reflection
6. Rotation
7. Translation
8. Translation
9. Rotation