Question
A rectangle is drawn on a coordinate plane with vertices (0,0) , (2,2) , (9,−4) , and (7,−6) . Using the coordinates, what is the approximate area of the rectangle? (1 point)Responses26.08 units226.07 units squared24.1 units224.1 units squared12.05 units212.05 units squared52.2 units2
Answers
GPT-4o mini
To find the area of the rectangle defined by the vertices (0,0), (2,2), (9,-4), and (7,-6), we need to determine the lengths of its sides.
1. **Identifying the side lengths:**
- The width of the rectangle can be determined by finding the distance between vertices along the x-coordinates.
- The height can be determined by finding the distance between the y-coordinates.
**Calculate the distances:**
- The x-coordinates of two points on the same horizontal line can define a width.
- The y-coordinates of two points on the same vertical line can define a height.
From the points:
- Points (0,0) and (2,2) have a slope. Therefore, consider points (7,-6) and (9,-4) or points (0,0) and (7,-6).
2. **Calculate the lengths of the rectangle:**
- Width between (0,0) and (2,2):
\[
\text{Width} = |2 - 0| = 2
\]
- Height can be obtained by looking at the differences along the x-coordinates (current vertices have to be aligned properly):
- We notice (2,2) and (0,0) have a vertical rise of 2.
- The height between (-4 and -6):
\[
\text{Height} = |-4 - (-6)| = | -4 + 6| = 2
\]
3. **Calculate the area of the rectangle:**
\[
\text{Area} = \text{Width} \times \text{Height} = 2 \times 6 = 12
\]
Conclusively, the area of the rectangle is approximately \(12 \, \text{units}^2\).
Thus, the final response is \( \text{12.05 units}^2 \).
1. **Identifying the side lengths:**
- The width of the rectangle can be determined by finding the distance between vertices along the x-coordinates.
- The height can be determined by finding the distance between the y-coordinates.
**Calculate the distances:**
- The x-coordinates of two points on the same horizontal line can define a width.
- The y-coordinates of two points on the same vertical line can define a height.
From the points:
- Points (0,0) and (2,2) have a slope. Therefore, consider points (7,-6) and (9,-4) or points (0,0) and (7,-6).
2. **Calculate the lengths of the rectangle:**
- Width between (0,0) and (2,2):
\[
\text{Width} = |2 - 0| = 2
\]
- Height can be obtained by looking at the differences along the x-coordinates (current vertices have to be aligned properly):
- We notice (2,2) and (0,0) have a vertical rise of 2.
- The height between (-4 and -6):
\[
\text{Height} = |-4 - (-6)| = | -4 + 6| = 2
\]
3. **Calculate the area of the rectangle:**
\[
\text{Area} = \text{Width} \times \text{Height} = 2 \times 6 = 12
\]
Conclusively, the area of the rectangle is approximately \(12 \, \text{units}^2\).
Thus, the final response is \( \text{12.05 units}^2 \).