Question
Find the coordinates of the rectangle and use them to compute the area. (1 point) Responses 16 units2 16 units squared 15 units2 15 units squared 30 units2 30 units squared 8 units2
The square's coordinates are, A: (-5, 6) B: (-2, 6) D: (-5, 1) C: (-1, 1)
The square's coordinates are, A: (-5, 6) B: (-2, 6) D: (-5, 1) C: (-1, 1)
Answers
Answered by
GPT-4o mini
To find the area of the rectangle using the given coordinates, we need to identify the vertices of the rectangle and calculate the lengths of its sides.
The coordinates provided are:
- A: (-5, 6)
- B: (-2, 6)
- C: (-1, 1)
- D: (-5, 1)
**Step 1: Identify the vertices of the rectangle.**
From the coordinates, we can see that:
- Vertices A and B have the same y-coordinate (6), indicating they are along the top side of the rectangle.
- Vertices C and D have the same y-coordinate (1), indicating they are along the bottom side.
- The x-coordinates of A and D are both -5, while the x-coordinates of B and C are different.
**Step 2: Calculate the length and width of the rectangle.**
- **Length (horizontal distance between A and B):**
\[
|x_B - x_A| = |-2 - (-5)| = |-2 + 5| = 3 \text{ units}
\]
- **Width (vertical distance between A and D):**
\[
|y_A - y_D| = |6 - 1| = 5 \text{ units}
\]
**Step 3: Calculate the area of the rectangle.**
The area \(A\) of a rectangle is given by:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the values we found:
\[
A = 3 \text{ units} \times 5 \text{ units} = 15 \text{ units}^2
\]
Thus, the area of the rectangle is **15 units²**.
The correct response from the options provided is **15 units²** or **15 units squared**.
The coordinates provided are:
- A: (-5, 6)
- B: (-2, 6)
- C: (-1, 1)
- D: (-5, 1)
**Step 1: Identify the vertices of the rectangle.**
From the coordinates, we can see that:
- Vertices A and B have the same y-coordinate (6), indicating they are along the top side of the rectangle.
- Vertices C and D have the same y-coordinate (1), indicating they are along the bottom side.
- The x-coordinates of A and D are both -5, while the x-coordinates of B and C are different.
**Step 2: Calculate the length and width of the rectangle.**
- **Length (horizontal distance between A and B):**
\[
|x_B - x_A| = |-2 - (-5)| = |-2 + 5| = 3 \text{ units}
\]
- **Width (vertical distance between A and D):**
\[
|y_A - y_D| = |6 - 1| = 5 \text{ units}
\]
**Step 3: Calculate the area of the rectangle.**
The area \(A\) of a rectangle is given by:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the values we found:
\[
A = 3 \text{ units} \times 5 \text{ units} = 15 \text{ units}^2
\]
Thus, the area of the rectangle is **15 units²**.
The correct response from the options provided is **15 units²** or **15 units squared**.
Answer
My bad, C's coordinates are (-2, 1)
Answered by
GPT-4o mini
No problem! Let's recalculate the area of the rectangle with the updated coordinates for C.
The revised coordinates are:
- A: (-5, 6)
- B: (-2, 6)
- C: (-2, 1)
- D: (-5, 1)
**Step 1: Identify the vertices of the rectangle.**
- Vertices A and B (top side of the rectangle) have the same y-coordinate (6).
- Vertices C and D (bottom side of the rectangle) have the same y-coordinate (1).
- The x-coordinates of A and D are both -5, while the x-coordinates of B and C are both -2.
**Step 2: Calculate the length and width of the rectangle.**
- **Length (horizontal distance between A and B):**
\[
|x_B - x_A| = |-2 - (-5)| = |-2 + 5| = 3 \text{ units}
\]
- **Width (vertical distance between A and D, or between C and B):**
\[
|y_A - y_D| = |6 - 1| = 5 \text{ units}
\]
**Step 3: Calculate the area of the rectangle.**
The area \(A\) of a rectangle is given by:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the values we found:
\[
A = 3 \text{ units} \times 5 \text{ units} = 15 \text{ units}^2
\]
So, the area of the rectangle is still **15 units²**.
The correct response from your options is **15 units²** or **15 units squared**.
The revised coordinates are:
- A: (-5, 6)
- B: (-2, 6)
- C: (-2, 1)
- D: (-5, 1)
**Step 1: Identify the vertices of the rectangle.**
- Vertices A and B (top side of the rectangle) have the same y-coordinate (6).
- Vertices C and D (bottom side of the rectangle) have the same y-coordinate (1).
- The x-coordinates of A and D are both -5, while the x-coordinates of B and C are both -2.
**Step 2: Calculate the length and width of the rectangle.**
- **Length (horizontal distance between A and B):**
\[
|x_B - x_A| = |-2 - (-5)| = |-2 + 5| = 3 \text{ units}
\]
- **Width (vertical distance between A and D, or between C and B):**
\[
|y_A - y_D| = |6 - 1| = 5 \text{ units}
\]
**Step 3: Calculate the area of the rectangle.**
The area \(A\) of a rectangle is given by:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the values we found:
\[
A = 3 \text{ units} \times 5 \text{ units} = 15 \text{ units}^2
\]
So, the area of the rectangle is still **15 units²**.
The correct response from your options is **15 units²** or **15 units squared**.