Answered

The upper-left coordinates of a rectangle are (-1, 7), and the upper-right coordinates are (4, 7). The rectangle has an area of 20 square units.

Draw the rectangle on the coordinate plane below.

```
y
8
7
6
5
4
3
2
1
0
-1 0 1 2 3 4 5 6 7 8
```



Answer :

GinnyAnswer
To draw the rectangle on the coordinate plane, we can proceed step by step by first establishing the given coordinates and then finding the dimensions and other vertices of the rectangle.

### Step-by-Step Solution

1. Given Coordinates of the Upper Veritices:
- Upper-left corner is at [tex]\((-1, 7)\)[/tex].
- Upper-right corner is at [tex]\((4, 7)\)[/tex].

2. Calculate the Width:
- The width of the rectangle is the horizontal distance between the upper-left and upper-right vertices.
- The x-coordinate of the upper-left corner is [tex]\(-1\)[/tex].
- The x-coordinate of the upper-right corner is [tex]\(4\)[/tex].
- Width = [tex]\(4 - (-1) = 5\)[/tex] units.

3. Calculate the Height:
- The area of the rectangle is given to be 20 square units.
- The area of a rectangle is given by the formula:
[tex]\[ \text{Area} = \text{Width} \times \text{Height} \][/tex]
- Substituting the known values:
[tex]\[ 20 = 5 \times \text{Height} \][/tex]
- To find the height:
[tex]\[ \text{Height} = \frac{20}{5} = 4 \][/tex] units.

4. Find the Lower Vertices:
- Knowing the height of the rectangle, we can determine the y-coordinates of the lower vertices, as they will be 4 units down from the upper vertices.
- Lower-left corner:
- x-coordinate: Same as the upper-left, which is [tex]\(-1\)[/tex].
- y-coordinate: [tex]\(7 - 4 = 3\)[/tex].
- Lower-left corner is at [tex]\((-1, 3)\)[/tex].

- Lower-right corner:
- x-coordinate: Same as the upper-right, which is [tex]\(4\)[/tex].
- y-coordinate: [tex]\(7 - 4 = 3\)[/tex].
- Lower-right corner is at [tex]\((4, 3)\)[/tex].

5. Coordinates of All Vertices:
- Upper-left: [tex]\((-1, 7)\)[/tex]
- Upper-right: [tex]\((4, 7)\)[/tex]
- Lower-left: [tex]\((-1, 3)\)[/tex]
- Lower-right: [tex]\((4, 3)\)[/tex]

### Drawing the Rectangle:
Using the calculated coordinates, plot the rectangle on the coordinate plane:

1. Start by marking the upper-left corner at [tex]\((-1, 7)\)[/tex].
2. Mark the upper-right corner at [tex]\((4, 7)\)[/tex].
3. Mark the lower-left corner at [tex]\((-1, 3)\)[/tex].
4. Mark the lower-right corner at [tex]\((4, 3)\)[/tex].

Connect the dots to form a rectangle.

Here's a rough visualization:

```
y
8 |
7 | (4, 7)
6 |
5 |
4 |
3 | (4, 3)
2 |
1 |
0 |
- +
-1 0 1 2 3 4 x
```

This rectangle sits on the coordinate plane with the vertices as calculated.

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