Use the coordinates to compute the approximate area of the rectangle. Round to the nearest whole number

Question

Coordinates: (1,1), (0,2), (2,4), (3,3)
A. 32
B. 6
C. 8
D. 4

Answer 1

To compute the approximate area of the rectangle defined by the coordinates (1,1), (0,2), (2,4), and (3,3), we first need to identify which points correspond to the vertices of a rectangle.

However, the provided coordinates do not clearly form a rectangle since they do not satisfy the properties of a rectangle (four right angles and opposite sides being equal in length). Instead, we can represent the area of the polygon formed by these points.

Let's plot the points:

• (1,1)
• (0,2)
• (2,4)
• (3,3)

To compute the area of the polygon formed by these points, we can use the shoelace formula, also known as Gauss's area formula. Here, we will list the coordinates in order and then apply the formula.

For this calculation, we can use an order such as (1,1), (0,2), (3,3), (2,4) (you can order them in a different manner, but it has to loop around the polygon):

Let's arrange the points:

1. (1, 1)
2. (0, 2)
3. (3, 3)
4. (2, 4)

We repeat the first point at the bottom:

1. (1, 1)

Now we apply the shoelace formula: Area = 1/2 * |(x1y2 + x2y3 + x3y4 + x4y5) - (y1x2 + y2x3 + y3x4 + y4x1)|

Calculating:

• Assign:
  • (x1, y1) = (1, 1)
  • (x2, y2) = (0, 2)
  • (x3, y3) = (3, 3)
  • (x4, y4) = (2, 4)

Now compute:

1. For the first term: (1 * 2) + (0 * 3) + (3 * 4) + (2 * 1) = 2 + 0 + 12 + 2 = 16
2. For the second term: (1 * 0) + (2 * 3) + (3 * 2) + (4 * 1) = 0 + 6 + 6 + 4 = 16

Thus: Area = 1/2 * |16 - 16| = 1/2 * 0 = 0

This indicates that the points may not outline a polygon with a well-defined area (they may fall on a straight line or form a disjointed polygon). Since I cannot directly form an area from the coordinates as given, I recommend verifying the correctness of the coordinates against the requirement of forming a rectangle.

In simplest terms based on the given options, the closest reasonable area that might be sought after among those numbers could lead to a misunderstanding. Would you need a correction in the coordinates or a different approach regarding the shape related to those coordinates?

Answer 2

you have to choose an option

Answer 3

Given the provided coordinates and the options available, if I have to select an approximate area based on the assumption that these coordinates form some type of polygon, I would suggest the following:

The coordinates do not form a perfect rectangle, and computing the area yields a result that suggests they may not create a tangible area at all.

However, if we consider the bounding box that could encompass the given coordinates:

• The minimum x-coordinate is 0 and the maximum x-coordinate is 3.
• The minimum y-coordinate is 1 and the maximum y-coordinate is 4.

The bounding rectangle can be calculated as:

• Width = (max x - min x) = 3 - 0 = 3
• Height = (max y - min y) = 4 - 1 = 3

Thus, the area of the bounding rectangle = Width × Height = 3 × 3 = 9.

Since your options are limited, and 9 isn't provided, the most reasonable estimate among the options for the area is:

C. 8

This value is the closest approximation to the computed bounding area.