Use the coordinates to compute the approximate area of the rectangle. Round your answer to the nearest whole number. (1 point) units2

Question

A 4, 2
B 10, 4
C 6, 16
D 0, 14

Answer 1

To compute the area of the rectangle formed by the given points A, B, C, and D, we first need to identify the rectangle's corners and then determine the length and width.

We have the following coordinates:

• A \( (4, 2) \)
• B \( (10, 4) \)
• C \( (6, 16) \)
• D \( (0, 14) \)

Step 1: Identify the Rectangle

We can sort the points to identify which two pairs of points form the opposite corners of the rectangle. Points A and D appear to be on the left-hand side (A lower than D), while points B and C appear to be higher up on the right side.

To calculate the dimensions, we can take the extreme x-coordinates and the extreme y-coordinates:

• The minimum x-coordinate is from point D \( (0, 14) \) ⇒ \( x_{\text{min}} = 0 \)
• The maximum x-coordinate is from point B \( (10, 4) \) ⇒ \( x_{\text{max}} = 10 \)
• The minimum y-coordinate is from point A \( (4, 2) \) ⇒ \( y_{\text{min}} = 2 \)
• The maximum y-coordinate is from point C \( (6, 16) \) ⇒ \( y_{\text{max}} = 16 \)

Step 2: Calculate Length and Width

• Length (along x-axis) \( = x_{\text{max}} - x_{\text{min}} = 10 - 0 = 10 \)
• Width (along y-axis) \( = y_{\text{max}} - y_{\text{min}} = 16 - 2 = 14 \)

Step 3: Calculate Area

The area \( A \) of the rectangle is given by: \[ A = \text{Length} \times \text{Width} = 10 \times 14 = 140 \]

Final Answer

Thus, the approximate area of the rectangle, rounded to the nearest whole number, is: \[ \boxed{140} \text{ units}^2 \]

Answer 2

that's wrong

Answer 3

I apologize if there was an oversight in my calculations. Let’s go through the coordinates and calculations again to ensure accuracy.

We have the points:

• A \( (4, 2) \)
• B \( (10, 4) \)
• C \( (6, 16) \)
• D \( (0, 14) \)

Since we want to define a rectangle, we need to find corners that fit the properties of a rectangle, where two opposite points share the same x or y coordinates.

Step 1: Identifying Rectangle Corners

Examining the points, we can pair them logically based on their coordinates:

• Points A \( (4, 2) \) and B \( (10, 4) \) have different y-values. Similarly, C \( (6, 16) \) and D \( (0, 14) \) have different x-values. This shows that they do not directly form a rectangle.

For simplicity, let's first find the boundaries of the rectangle using these points just to ensure we use the right pairs:

• Minimum x: \( x_{\text{min}} = 0 \) (from D)
• Maximum x: \( x_{\text{max}} = 10 \) (from B)
• Minimum y: \( y_{\text{min}} = 2 \) (from A)
• Maximum y: \( y_{\text{max}} = 16 \) (from C)

Step 2: Calculating Length and Width

• The length of the rectangle (along the x-axis) is given by: \[ \text{Length} = x_{\text{max}} - x_{\text{min}} = 10 - 0 = 10 \]

• The width of the rectangle (along the y-axis) is given by: \[ \text{Width} = y_{\text{max}} - y_{\text{min}} = 16 - 2 = 14 \]

Step 3: Area of the Rectangle

Now compute the area: \[ \text{Area} = \text{Length} \times \text{Width} = 10 \times 14 = 140 \]

Final Confirmation:

The area of the rectangle computed through these points turned out to be \( 140 \) square units. If there’s a specific interpretation or need regarding how they should be connected to form a rectangle, please provide further details so I can assist more accurately. Otherwise, given this breakdown, the computed area stands at: \[ \boxed{140} \text{ units}^2 \]

If there is a specific definition or actual corners leading you to believe there's a mistake in identifying adjacent points of a rectangle, please clarify!