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Sagot :
To graph the quadrilateral with the given vertices [tex]\((-1, 6)\)[/tex], [tex]\((10, 1)\)[/tex], [tex]\((9, 5)\)[/tex], and [tex]\((7, 7)\)[/tex], follow these steps:
### Step-by-Step Solution
1. Plot the Points:
Start by plotting each of the given vertices on a coordinate plane.
- Point A: [tex]\((-1, 6)\)[/tex]
- Point B: [tex]\((10, 1)\)[/tex]
- Point C: [tex]\((9, 5)\)[/tex]
- Point D: [tex]\((7, 7)\)[/tex]
2. Label the Points:
- Clearly label each of the vertices with their corresponding coordinates.
3. Connect the Points:
- Draw straight lines to connect the vertices in the order you want them to form the quadrilateral. For this example, we can connect them in the given order:
1. Connect point A [tex]\((-1, 6)\)[/tex] to point B [tex]\((10, 1)\)[/tex].
2. Connect point B [tex]\((10, 1)\)[/tex] to point C [tex]\((9, 5)\)[/tex].
3. Connect point C [tex]\((9, 5)\)[/tex] to point D [tex]\((7, 7)\)[/tex].
4. Finally, connect point D [tex]\((7, 7)\)[/tex] back to point A [tex]\((-1, 6)\)[/tex].
### Visual Representation
1. Draw the Axes:
- Draw the x-axis and y-axis on your graph paper or coordinate plane.
- Make sure to appropriately scale the axes. Since the x-coordinates range from [tex]\(-1\)[/tex] to [tex]\(10\)[/tex] and the y-coordinates range from [tex]\(1\)[/tex] to [tex]\(7\)[/tex], ensure that these ranges are covered.
2. Plotting the Points:
- Point A: Move [tex]\(1\)[/tex] unit to the left from the origin (0,0) and [tex]\(6\)[/tex] units up. Mark this point.
- Point B: Move [tex]\(10\)[/tex] units to the right and [tex]\(1\)[/tex] unit up. Mark this point.
- Point C: Move [tex]\(9\)[/tex] units to the right and [tex]\(5\)[/tex] units up. Mark this point.
- Point D: Move [tex]\(7\)[/tex] units to the right and [tex]\(7\)[/tex] units up. Mark this point.
3. Connecting the Points:
- Draw a line from point A [tex]\((-1, 6)\)[/tex] to point B [tex]\((10, 1)\)[/tex].
- Draw a line from point B [tex]\((10, 1)\)[/tex] to point C [tex]\((9, 5)\)[/tex].
- Draw a line from point C [tex]\((9, 5)\)[/tex] to point D [tex]\((7, 7)\)[/tex].
- Draw a line from point D [tex]\((7, 7)\)[/tex] back to point A [tex]\((-1, 6)\)[/tex].
### Final Graph:
- The quadrilateral should now be visible on your coordinate plane, and it should have the shape formed by the connected points [tex]\((-1, 6)\)[/tex], [tex]\((10, 1)\)[/tex], [tex]\((9, 5)\)[/tex], and [tex]\((7, 7)\)[/tex].
By following these steps, you can successfully graph the given quadrilateral on the coordinate plane.
### Step-by-Step Solution
1. Plot the Points:
Start by plotting each of the given vertices on a coordinate plane.
- Point A: [tex]\((-1, 6)\)[/tex]
- Point B: [tex]\((10, 1)\)[/tex]
- Point C: [tex]\((9, 5)\)[/tex]
- Point D: [tex]\((7, 7)\)[/tex]
2. Label the Points:
- Clearly label each of the vertices with their corresponding coordinates.
3. Connect the Points:
- Draw straight lines to connect the vertices in the order you want them to form the quadrilateral. For this example, we can connect them in the given order:
1. Connect point A [tex]\((-1, 6)\)[/tex] to point B [tex]\((10, 1)\)[/tex].
2. Connect point B [tex]\((10, 1)\)[/tex] to point C [tex]\((9, 5)\)[/tex].
3. Connect point C [tex]\((9, 5)\)[/tex] to point D [tex]\((7, 7)\)[/tex].
4. Finally, connect point D [tex]\((7, 7)\)[/tex] back to point A [tex]\((-1, 6)\)[/tex].
### Visual Representation
1. Draw the Axes:
- Draw the x-axis and y-axis on your graph paper or coordinate plane.
- Make sure to appropriately scale the axes. Since the x-coordinates range from [tex]\(-1\)[/tex] to [tex]\(10\)[/tex] and the y-coordinates range from [tex]\(1\)[/tex] to [tex]\(7\)[/tex], ensure that these ranges are covered.
2. Plotting the Points:
- Point A: Move [tex]\(1\)[/tex] unit to the left from the origin (0,0) and [tex]\(6\)[/tex] units up. Mark this point.
- Point B: Move [tex]\(10\)[/tex] units to the right and [tex]\(1\)[/tex] unit up. Mark this point.
- Point C: Move [tex]\(9\)[/tex] units to the right and [tex]\(5\)[/tex] units up. Mark this point.
- Point D: Move [tex]\(7\)[/tex] units to the right and [tex]\(7\)[/tex] units up. Mark this point.
3. Connecting the Points:
- Draw a line from point A [tex]\((-1, 6)\)[/tex] to point B [tex]\((10, 1)\)[/tex].
- Draw a line from point B [tex]\((10, 1)\)[/tex] to point C [tex]\((9, 5)\)[/tex].
- Draw a line from point C [tex]\((9, 5)\)[/tex] to point D [tex]\((7, 7)\)[/tex].
- Draw a line from point D [tex]\((7, 7)\)[/tex] back to point A [tex]\((-1, 6)\)[/tex].
### Final Graph:
- The quadrilateral should now be visible on your coordinate plane, and it should have the shape formed by the connected points [tex]\((-1, 6)\)[/tex], [tex]\((10, 1)\)[/tex], [tex]\((9, 5)\)[/tex], and [tex]\((7, 7)\)[/tex].
By following these steps, you can successfully graph the given quadrilateral on the coordinate plane.
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