Answer :
Let's answer the question step-by-step.
A. Graphing the Points:
First, we'll plot the points [tex]\((1, -1)\)[/tex], [tex]\((4, -1)\)[/tex], [tex]\((4, -8)\)[/tex], and [tex]\((1, -8)\)[/tex] on a coordinate plane.
- [tex]\((1, -1)\)[/tex]: This is 1 unit to the right of the origin on the x-axis and 1 unit down on the y-axis.
- [tex]\((4, -1)\)[/tex]: This is 4 units to the right of the origin on the x-axis and 1 unit down on the y-axis.
- [tex]\((4, -8)\)[/tex]: This is 4 units to the right of the origin on the x-axis and 8 units down on the y-axis.
- [tex]\((1, -8)\)[/tex]: This is 1 unit to the right of the origin on the x-axis and 8 units down on the y-axis.
Next, we connect these points in the given order to form a rectangle.
B. Calculating the Length and Width:
1. To find the width, we look at the distance between the points [tex]\((1, -1)\)[/tex] and [tex]\((4, -1)\)[/tex] (or [tex]\((1, -8)\)[/tex] and [tex]\((4, -8)\)[/tex]).
- The x-coordinates change from 1 to 4, so the width is [tex]\(|4 - 1| = 3\)[/tex] units.
2. To find the length, we look at the distance between the points [tex]\((4, -1)\)[/tex] and [tex]\((4, -8)\)[/tex] (or [tex]\((1, -1)\)[/tex] and [tex]\((1, -8)\)[/tex]).
- The y-coordinates change from -1 to -8, so the length is [tex]\(|-1 - (-8)| = |-1 + 8| = 7\)[/tex] units.
Length of the rectangle: 7 units
Width of the rectangle: 3 units
C. Finding the Perimeter:
The perimeter [tex]\(P\)[/tex] of a rectangle is given by the formula:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
Substituting the values we found:
[tex]\[ P = 2 \times (7 + 3) = 2 \times 10 = 20 \][/tex]
Perimeter of the rectangle: 20 units
D. Finding the Area:
The area [tex]\(A\)[/tex] of a rectangle is given by the formula:
[tex]\[ A = \text{length} \times \text{width} \][/tex]
Substituting the values we found:
[tex]\[ A = 7 \times 3 = 21 \][/tex]
Area of the rectangle: 21 square units
So, summarizing everything:
A. Graph the points [tex]\((1, -1)\)[/tex], [tex]\((4, -1)\)[/tex], [tex]\((4, -8)\)[/tex], and [tex]\((1, -8)\)[/tex]; connect them in order to form a rectangle.
B. Length = 7 units, Width = 3 units.
C. Perimeter [tex]\(P\)[/tex] = 20 units.
D. Area [tex]\(A\)[/tex] = 21 square units.
A. Graphing the Points:
First, we'll plot the points [tex]\((1, -1)\)[/tex], [tex]\((4, -1)\)[/tex], [tex]\((4, -8)\)[/tex], and [tex]\((1, -8)\)[/tex] on a coordinate plane.
- [tex]\((1, -1)\)[/tex]: This is 1 unit to the right of the origin on the x-axis and 1 unit down on the y-axis.
- [tex]\((4, -1)\)[/tex]: This is 4 units to the right of the origin on the x-axis and 1 unit down on the y-axis.
- [tex]\((4, -8)\)[/tex]: This is 4 units to the right of the origin on the x-axis and 8 units down on the y-axis.
- [tex]\((1, -8)\)[/tex]: This is 1 unit to the right of the origin on the x-axis and 8 units down on the y-axis.
Next, we connect these points in the given order to form a rectangle.
B. Calculating the Length and Width:
1. To find the width, we look at the distance between the points [tex]\((1, -1)\)[/tex] and [tex]\((4, -1)\)[/tex] (or [tex]\((1, -8)\)[/tex] and [tex]\((4, -8)\)[/tex]).
- The x-coordinates change from 1 to 4, so the width is [tex]\(|4 - 1| = 3\)[/tex] units.
2. To find the length, we look at the distance between the points [tex]\((4, -1)\)[/tex] and [tex]\((4, -8)\)[/tex] (or [tex]\((1, -1)\)[/tex] and [tex]\((1, -8)\)[/tex]).
- The y-coordinates change from -1 to -8, so the length is [tex]\(|-1 - (-8)| = |-1 + 8| = 7\)[/tex] units.
Length of the rectangle: 7 units
Width of the rectangle: 3 units
C. Finding the Perimeter:
The perimeter [tex]\(P\)[/tex] of a rectangle is given by the formula:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
Substituting the values we found:
[tex]\[ P = 2 \times (7 + 3) = 2 \times 10 = 20 \][/tex]
Perimeter of the rectangle: 20 units
D. Finding the Area:
The area [tex]\(A\)[/tex] of a rectangle is given by the formula:
[tex]\[ A = \text{length} \times \text{width} \][/tex]
Substituting the values we found:
[tex]\[ A = 7 \times 3 = 21 \][/tex]
Area of the rectangle: 21 square units
So, summarizing everything:
A. Graph the points [tex]\((1, -1)\)[/tex], [tex]\((4, -1)\)[/tex], [tex]\((4, -8)\)[/tex], and [tex]\((1, -8)\)[/tex]; connect them in order to form a rectangle.
B. Length = 7 units, Width = 3 units.
C. Perimeter [tex]\(P\)[/tex] = 20 units.
D. Area [tex]\(A\)[/tex] = 21 square units.
