Question

rotation 1
enter the coordinates of the points on the red figure and press submit.
(x,y)
submit
what do you notice?

Explanation:

Step1: Identify the left - most and bottom - most point

Looking at the red L - shaped figure, the left - most and bottom - most point (the corner of the horizontal and vertical parts) has a horizontal (x) coordinate of 2 (since it's 2 units to the right of the origin on the x - axis) and a vertical (y) coordinate of 2 (2 units above the origin on the y - axis). Wait, no, let's re - examine the grid. Each grid square is 1 unit. Let's list the vertices:

- The bottom - left vertex of the horizontal part: Let's count the x - coordinate. From the origin (0,0), moving right 2 units? Wait, no, looking at the grid, the red figure:

The horizontal part (the long rectangle) has a bottom - left corner at (2, 2)? Wait, no, let's look at the x - axis: the vertical line at x = 2, x = 5, etc. Wait, the red figure:

Let's find all the vertices:

1. The bottom - left vertex of the horizontal segment: Let's see, the x - coordinate: from 0, moving right 2 units? Wait, no, the grid lines are at x=-10, - 5, 0, 5, 10 and y=-10, - 5, 0, 5, 10.

Looking at the red figure:

- The bottom - left corner of the horizontal part: x = 2, y = 2? No, wait, the y - axis: the red figure is above the x - axis (y = 0). Let's check the y - coordinates. The bottom edge of the red figure is at y = 2? Wait, no, the grid has y = 0 as the middle line. Wait, the red figure is in the first quadrant (x>0, y>0).

Wait, let's list the vertices properly:

- Vertex 1: (2, 2) – no, wait, the horizontal part: from x = 2 to x = 5 (width 3 units) and y = 2 to y = 4 (height 2 units)? No, the vertical part (the square - like part) is from x = 5 to x = 7 (width 2 units) and y = 4 to y = 6 (height 2 units)? Wait, no, let's count the grid squares.

Each small square is 1 unit. Let's look at the red figure:

- The bottom - left vertex of the horizontal rectangle: x = 2, y = 2 (since it's 2 units right of x = 0 and 2 units above y = 0).

- The bottom - right vertex of the horizontal rectangle: x = 5, y = 2.

- The top - right vertex of the horizontal rectangle: x = 5, y = 4.

- The bottom - right vertex of the vertical rectangle: x = 7, y = 2.

- The top - right vertex of the vertical rectangle: x = 7, y = 6.

- The top - left vertex of the vertical rectangle: x = 5, y = 6.

- The top - left vertex of the horizontal rectangle: x = 2, y = 4.

Wait, maybe I'm overcomplicating. Let's use the grid:

Looking at the red figure, the key vertices (the corners) are:

(2, 2), (5, 2), (5, 4), (7, 4), (7, 6), (5, 6), (2, 6), (2, 4)? No, that doesn't form an L - shape. Wait, the L - shape: the horizontal part is from x = 2 to x = 5 (length 3) and y = 2 to y = 4 (height 2), and the vertical part is from x = 5 to x = 7 (length 2) and y = 4 to y = 6 (height 2), and also from x = 5 to x = 7 and y = 2 to y = 4? No, the red figure is an L - shape, so it has two rectangles: one horizontal (length 3, height 2) and one vertical (length 2, height 4) attached at the corner (5, 4).

So the vertices are:

1. (2, 2) – bottom - left of horizontal rectangle.

2. (5, 2) – bottom - right of horizontal rectangle.

3. (5, 6) – top - right of vertical rectangle.

4. (7, 6) – top - right of vertical rectangle.

5. (7, 2) – bottom - right of vertical rectangle. Wait, no, that would make a different shape. Wait, maybe the correct vertices are:

Looking at the graph, the red figure:

- The bottom - left corner: (2, 2)

- The bottom - right corner of the horizontal part: (5, 2)

- The top - right corner of the vertical part: (7, 6)

- The top - left corner of the vertical part: (5, 6)

- The top - left corner of the horizontal part: (2, 4)

Wait, this is getting confusing. Maybe the problem is to list the coordinates of the red figure's points. Let's assume the red figure has vertices at (2, 2), (5, 2), (5, 6), (7, 6), (7, 2), (2, 4), (2, 2)? No, that's not right.

Alternatively, maybe the red figure is a polygon with vertices:

(2, 2), (5, 2), (5, 4), (7, 4), (7, 6), (5, 6), (2, 6), (2, 4)

But perhaps the simpler way: let's look at the grid. The red figure is in the first quadrant. Let's take the bottom - left point: x = 2, y = 2; bottom - right of horizontal part: x = 5, y = 2; top - right of vertical part: x = 7, y = 6; top - left of vertical part: x = 5, y = 6; top - left of horizontal part: x = 2, y = 4.

So the coordinates of the red figure's points (vertices) are (2, 2), (5, 2), (5, 6), (7, 6), (7, 2), (2, 4), (2, 2) – no, that's a closed shape.

But maybe the problem is to enter the coordinates of the red figure's vertices. Let's list them correctly:

1. (2, 2)

2. (5, 2)

3. (5, 4)

4. (7, 4)

5. (7, 6)

6. (5, 6)

7. (2, 6)

8. (2, 4)

Wait, no, that's a rectangle with a notch? No, the red figure is an L - shape, so it's two rectangles: one 3 units long (x from 2 to 5) and 2 units tall (y from 2 to 4), and another 2 units long (x from 5 to 7) and 4 units tall (y from 2 to 6). So the vertices are:

- (2, 2), (5, 2), (5, 4), (7, 4), (7, 6), (5, 6), (2, 6), (2, 4)

Yes, that makes an L - shape.

Step2: Enter the coordinates

Now, we can enter these coordinates into the (x, y) table. For example, the first vertex is (2, 2), the second is (5, 2), the third is (5, 4), the fourth is (7, 4), the fifth is (7, 6), the sixth is (5, 6), the seventh is (2, 6), the eighth is (2, 4).

When we look at the coordinates, we can notice that for the horizontal part (y = 2 to y = 4, x = 2 to x = 5), the y - coordinate is between 2 and 4, and for the vertical part (x = 5 to x = 7, y = 2 to y = 6), the x - coordinate is between 5 and 7. Also, when we rotate the figure (though the problem says "Rotation 1", maybe after rotation, the coordinates will change, but for now, we list the coordinates of the red figure.

Answer:

The coordinates of the red figure's vertices (points) are (2, 2), (5, 2), (5, 4), (7, 4), (7, 6), (5, 6), (2, 6), (2, 4) (you can enter these into the table). When noticing, we can see that the figure is an L - shaped polygon with vertices at these coordinates, and if we were to rotate it (e.g., 90 degrees), the coordinates would transform according to rotation rules (e.g., (x,y)→(-y,x) for 90 - degree counterclockwise rotation about the origin, but here the center of rotation might be different). However, for the first part, the coordinates of the red figure's points are as listed.