To determine the type of transformation for each graph, we need to look at how the shape moved from its original position (pre-image) to its new position (image).
Here are the three main types of transformations:
1.
Translation (Slide): The shape slides in a specific direction without turning or flipping. 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 creates a mirror image.
3.
Rotation (Turn): The shape turns around a fixed point.
Let's analyze each problem step-by-step:
1. Triangle $ABC$ moves up and to the right to become triangle $A'B'C'$. The orientation stays the same (point $A$ is still the bottom-left corner relative to the shape). This is a slide.
*
Type: Translation
2. Triangle $MNO$ moves to the right to become triangle $M'N'O'$. The shape has not turned or flipped; it simply shifted along the x-axis.
*
Type: Translation
3. Segment $PQ$ moves up and to the right to become segment $P'Q'$. The slope and length remain identical, and it hasn't flipped. It is a slide.
*
Type: Translation
4. Parallelogram $ABCD$ moves straight down to become parallelogram $A'B'C'D'$. Every point moved down by the same distance.
*
Type: Translation
5. Segment $DE$ flips horizontally to become segment $D'E'$. Point $D$ was on the left and is now on the right ($D'$), while $E$ stayed near the center but mirrored. The shape is a mirror image across the vertical y-axis.
*
Type: Reflection
6. Triangle $JKL$ shrinks towards the origin to become triangle $J'K'L'$. The points $J', K', L'$ are closer to the center $(0,0)$ than $J, K, L$, but the angles and proportions stay the same. This is a resizing.
*
Type: Dilation
7. Triangle $ABC$ turns around the origin to become triangle $A'B'C'$. If you trace point $A$ to $A'$, it has rotated counter-clockwise. The shape is turned, not slid or flipped.
*
Type: Rotation
8. Trapezoid $GHIJ$ moves down and to the right to become trapezoid $G'H'I'J'$. The shape maintains its upright orientation; it just changed location.
*
Type: Translation
9. Line $MP$ crosses through the origin to become line $M'P'$. Specifically, point $M$ (top left) moved to $M'$ (top right) and $P$ (bottom left) moved to $P'$ (bottom right). Wait, looking closer at the arrows:
* Original line goes from Top-Left to Bottom-Right.
* New line goes from Top-Right to Bottom-Left.
* Actually, let's look at the points. $M$ is at $(-3, 3)$ and $M'$ is at $(3, 3)$. $P$ is at $(-3, -3)$? No, $P$ is at $(-3, -2)$ roughly? Let's check coordinates.
* $M = (-3, 3)$, $M' = (3, 3)$. This is a reflection across the y-axis.
* $P = (-3, -2)$? No, let's look at the intersection. They intersect at the origin? No, they intersect at $(0,0)$?
* Let's look at the labels carefully. The arrow for $M$ points away from the center. The arrow for $M'$ points away from the center.
* $M$ is in Quadrant II. $M'$ is in Quadrant I.
* $P$ is in Quadrant III. $P'$ is in Quadrant IV.
* The figure has been flipped horizontally across the y-axis.
*
Type: Reflection
Final Answer:
1. Translation
2. Translation
3. Translation
4. Translation
5. Reflection
6. Dilation
7. Rotation
8. Translation
9. Reflection
Parent Tip: Review the logic above to help your child master the concept of transformations math printables.
