Answered

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Alex is designing a rectangular piece of art. He uses the
points (1,-1), (4,-1), (4, -8), and (1, -8) to draw the
a rectangle on a coordinate plane to begin the piece.
A. Graph the points on the coordinate plane. Then
connect the points in the order they were given to
draw the rectangle.
B. What are the length and width of the rectangle?
Alex's art
C. Find the perimeter of the rectangle.
P =
D. Find the area of the rectangle.
A =
==
square units
units
-6-5-4-3-2-
2-
S
-3+
34
4
5
569396
9
-10-
>

Verified Answer :

GinnyAnswer

Let's answer the question step-by-step.

A. Graphing the Points:

First, we'll plot the points \(\((1, -1)\)\), \(\((4, -1)\)\), \(\((4, -8)\)\), and \(\((1, -8)\)\) on a coordinate plane.

- \(\((1, -1)\)\): This is 1 unit to the right of the origin on the x-axis and 1 unit down on the y-axis.
- \(\((4, -1)\)\): This is 4 units to the right of the origin on the x-axis and 1 unit down on the y-axis.
- \(\((4, -8)\)\): This is 4 units to the right of the origin on the x-axis and 8 units down on the y-axis.
- \(\((1, -8)\)\): 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 \(\((1, -1)\)\) and \(\((4, -1)\)\) (or \(\((1, -8)\)\) and \(\((4, -8)\)\)).
- The x-coordinates change from 1 to 4, so the width is \(\(|4 - 1| = 3\)\) units.

2. To find the length, we look at the distance between the points \(\((4, -1)\)\) and \(\((4, -8)\)\) (or \(\((1, -1)\)\) and \(\((1, -8)\)\)).
- The y-coordinates change from -1 to -8, so the length is \(\(|-1 - (-8)| = |-1 + 8| = 7\)\) units.

Length of the rectangle: 7 units
Width of the rectangle: 3 units

C. Finding the Perimeter:

The perimeter \(\(P\)\) of a rectangle is given by the formula:
\(\[ P = 2 \times (\text{length} + \text{width}) \]\)

Substituting the values we found:
\(\[ P = 2 \times (7 + 3) = 2 \times 10 = 20 \]\)

Perimeter of the rectangle: 20 units

D. Finding the Area:

The area \(\(A\)\) of a rectangle is given by the formula:
\(\[ A = \text{length} \times \text{width} \]\)

Substituting the values we found:
\(\[ A = 7 \times 3 = 21 \]\)

Area of the rectangle: 21 square units



So, summarizing everything:

A. Graph the points \(\((1, -1)\)\), \(\((4, -1)\)\), \(\((4, -8)\)\), and \(\((1, -8)\)\); connect them in order to form a rectangle.

B. Length = 7 units, Width = 3 units.

C. Perimeter \(\(P\)\) = 20 units.

D. Area \(\(A\)\) = 21 square units.

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