Practice geometric transformations: slide, flip, and turn with shapes on a grid.

To solve this worksheet, we need to understand three types of movements for shapes on a grid:

1. Slide (Translation): Move the shape up, down, left, or right without turning it or flipping it. The shape stays in the exact same orientation.
2. Flip (Reflection): Create a mirror image of the shape. Imagine there is a mirror line next to the shape; the new shape looks like the reflection in that mirror.
3. Turn (Rotation): Spin the shape around a point. Usually, this means turning it 90 degrees (a quarter turn) clockwise or counter-clockwise.

Let's go through each problem step-by-step.

Problem 1: Turn
* Original Shape: An arrow pointing to the left. It has a triangular head on the left and a rectangular tail on the right.
* Instruction: Turn. In these grids, "Turn" usually implies a 90-degree turn. Let's assume a standard clockwise turn unless the position suggests otherwise. However, looking at the empty grid space, we just need to draw the result of a turn.
* Action: If you turn a left-pointing arrow 90 degrees clockwise, it will point up. If you turn it 90 degrees counter-clockwise, it will point down. Often, "Turn" without specification in early geometry might imply a 90-degree turn. Let's look at the other problems to see if there's a pattern. Problem 4 is also "Turn". Problem 7 is "Turn".
* Let's re-evaluate standard conventions. Often, "Turn" means rotate 90 degrees. Let's look at the shape again. It's a kite-like shape or an arrow head.
* Actually, let's look closer at shape 1. It is a triangle attached to a rectangle? No, it looks like a single polygon resembling an arrow pointing left.
* Let's assume a 90-degree clockwise turn. The tip pointing Left would now point Up. The flat back on the Right would now be on the Bottom.
* *Alternative:* If it's a 90-degree counter-clockwise turn, the tip points Down.
* *Check:* Without a specific direction (CW/CCW), either is technically a "turn". However, in many workbooks, if not specified, it's often clockwise. Let's describe the orientation change clearly. The shape rotates so its orientation changes by 90 degrees.

Problem 2: Slide
* Original Shape: A hexagon-like shape pointing up. It has a flat bottom and a pointed top.
* Instruction: Slide.
* Action: Move the entire shape to a new position on the grid without changing which way it points. It should still point up. You can move it right, left, up, or down. Typically, you just copy the shape exactly into the empty grid area provided.

Problem 3: Flip
* Original Shape: An 'L' shape lying on its back. The long part is horizontal at the bottom, and the short part goes up on the left side.
* Instruction: Flip.
* Action: Create a mirror image. If you flip it horizontally (left-to-right), the vertical part that was on the left will now be on the right. The horizontal bottom stays at the bottom. So, it will look like a standard capital L.

Problem 4: Turn
* Original Shape: A 'T' shape standing upright.
* Instruction: Turn.
* Action: Rotate the T. If we turn it 90 degrees clockwise, the top bar of the T will point to the right, and the stem will point down. It will look like a T lying on its side.

Problem 5: Slide
* Original Shape: An envelope shape or a house roof with a box. It's a pentagon with a point at the top.
* Instruction: Slide.
* Action: Copy the shape exactly. Do not turn it. Do not flip it. Just move it to the new spot. The point stays at the top.

Problem 6: Flip
* Original Shape: An arrow pointing to the right. Or a pencil shape pointing right.
* Instruction: Flip.
* Action: Create a mirror image. The tip pointing right will now point left. The flat end on the left will now be on the right.

Problem 7: Turn
* Original Shape: An upward-pointing arrow inside a square base? No, it looks like a simple house shape or an arrow pointing up. Let's call it an upward arrow.
* Instruction: Turn.
* Action: Rotate 90 degrees. If turned clockwise, the arrow pointing up will now point right.

Problem 8: Slide
* Original Shape: An 'L' shape standing upright. Vertical part on the left, horizontal part at the bottom going right.
* Instruction: Slide.
* Action: Copy the shape exactly. Move it to the new position. It remains an upright L.

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Summary of Actions for the Student:

1. Turn (Left Arrow): Draw the shape rotated 90 degrees. The tip will point Up (if clockwise) or Down (if counter-clockwise). *Standard answer is usually clockwise rotation.* -> Tip points Up.
2. Slide (Upward Hexagon): Draw the exact same shape in the new box. Tip points Up.
3. Flip (Backward L): Mirror it left-to-right. The vertical line moves to the right side. -> Looks like a normal L.
4. Turn (Upright T): Rotate 90 degrees. The top bar becomes vertical on the right side? No. The top bar is horizontal. When you rotate a T 90 deg clockwise, the top bar becomes vertical? No.
* Let's visualize T. Top bar is `---`. Stem is `|`.
* Rotate 90 deg CW: The `---` becomes `|` (vertical). The `|` stem becomes `-` (horizontal) pointing left?
* Let's trace coordinates. Center at (0,0). Top bar ends at (-1, 1) and (1, 1). Stem goes to (0, -1).
* Rotate 90 deg CW: (x,y) -> (y, -x).
* (-1, 1) -> (1, 1). (1, 1) -> (1, -1). So the "top bar" is now a vertical line on the right side from y=1 to y=-1.
* Stem (0, -1) -> (-1, 0). So the stem points to the left.
* Result: A vertical line on the right, with a short line sticking out to the left from the middle. It looks like a backward 'E' without the top and bottom bars? No, it looks like a T lying on its side, facing left.
* Wait, simpler view: Hold a paper T. Turn it clockwise. The top faces Right. The stem points Down. NO.
* Let's try again. T shape. Top is horizontal. Stem is vertical down.
* Turn 90 deg Clockwise: The "Top" (which was North) is now East (Right). The "Stem" (which was South) is now West (Left).
* So, the long part of the T is now vertical? No. The crossbar of the T is the wide part.
* Original: Crossbar is Horizontal. Stem is Vertical.
* Rotated 90 deg: Crossbar becomes Vertical. Stem becomes Horizontal.
* Direction: The top of the T points Right. The bottom of the stem points Left.
* So it looks like a T lying on its side, pointing to the Right.

5. Slide (Upward Pentagon): Draw the exact same shape. Point is Up.
6. Flip (Right Arrow): Mirror it. The arrow now points Left.
7. Turn (Up Arrow): Rotate 90 deg Clockwise. The arrow now points Right.
8. Slide (Upright L): Draw the exact same shape. L is upright.

Final Answer:

Here are the descriptions of how to draw each shape in the empty grids:

1. Turn: Draw the arrow shape rotated 90 degrees clockwise. The point of the arrow should face UP.
2. Slide: Draw the exact same hexagon shape. Do not change its direction. The point should still face UP.
3. Flip: Draw a mirror image of the L-shape. The vertical part of the L should now be on the RIGHT side (it will look like a normal capital L).
4. Turn: Draw the T-shape rotated 90 degrees clockwise. The top of the T should point to the RIGHT, and the stem should point to the LEFT. (It looks like a T lying on its side).
5. Slide: Draw the exact same house/envelope shape. Do not change its direction. The point should still face UP.
6. Flip: Draw a mirror image of the arrow. The arrow should now point to the LEFT.
7. Turn: Draw the arrow shape rotated 90 degrees clockwise. The arrow should now point to the RIGHT.
8. Slide: Draw the exact same L-shape. Do not change its direction. It should look like a normal capital L (vertical part on the left, horizontal part on the bottom).