Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
What is the coordinate matrix that describes the following quadrilateral ABCD?
![Below is a series of multiple-choice questions related to matrix selection. Each option displays a 2x4 matrix contained within square brackets.
---
### Choose the correct matrix:
**Option 1:**
\[
\begin{bmatrix}
3 & 3 & -4 & -4 \\
-1 & 5 & 5 & -1 \\
\end{bmatrix}
\]
(O)
**Option 2:**
\[
\begin{bmatrix}
1 & 5 & 5 & 1 \\
3 & 3 & -4 & -4 \\
\end{bmatrix}
\]
(O)
**Option 3:**
\[
\begin{bmatrix}
3 & 3 & -4 & -4 \\
1 & 5 & 5 & 1 \\
\end{bmatrix}
\]
(O)
**Option 4:**
\[
\begin{bmatrix}
3 & 3 & 4 & 4 \\
1 & 5 & 5 & 1 \\
\end{bmatrix}
\]
(O)
---
Ensure you carefully evaluate each matrix to select the one that is being asked for in your specific question or exercise. Each matrix is comprised of two rows and four columns, with a combination of positive and negative integers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d0c88f8-9b0e-4a87-ae6c-39dd67e2599b%2Ffc3a33d2-2e56-424e-a104-91f17b159194%2Fkt76htj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Below is a series of multiple-choice questions related to matrix selection. Each option displays a 2x4 matrix contained within square brackets.
---
### Choose the correct matrix:
**Option 1:**
\[
\begin{bmatrix}
3 & 3 & -4 & -4 \\
-1 & 5 & 5 & -1 \\
\end{bmatrix}
\]
(O)
**Option 2:**
\[
\begin{bmatrix}
1 & 5 & 5 & 1 \\
3 & 3 & -4 & -4 \\
\end{bmatrix}
\]
(O)
**Option 3:**
\[
\begin{bmatrix}
3 & 3 & -4 & -4 \\
1 & 5 & 5 & 1 \\
\end{bmatrix}
\]
(O)
**Option 4:**
\[
\begin{bmatrix}
3 & 3 & 4 & 4 \\
1 & 5 & 5 & 1 \\
\end{bmatrix}
\]
(O)
---
Ensure you carefully evaluate each matrix to select the one that is being asked for in your specific question or exercise. Each matrix is comprised of two rows and four columns, with a combination of positive and negative integers.
![### Understanding Coordinate Matrices for Quadrilaterals
#### Problem Statement
**Question:** What is the coordinate matrix that describes the following quadrilateral ABDC?
#### Diagram Explanation
The diagram provided displays a rectangle plotted on a Cartesian coordinate system. Each corner of the rectangle is marked with a blue dot and is labeled with the points A, B, C, and D as follows:
- Point A: Located at the bottom-right corner.
- Point B: Located at the top-right corner.
- Point C: Located at the top-left corner.
- Point D: Located at the bottom-left corner.
The coordinates for each point are as follows:
- A (5, 1)
- B (5, 4.5)
- D (1.5, 1)
- C (1.5, 4.5)
#### Coordinate Matrix Description
The coordinate matrix for the quadrilateral ABDC can be represented in the following manner:
\[
\begin{bmatrix}
A_x & B_x & D_x & C_x \\
A_y & B_y & D_y & C_y
\end{bmatrix}
=
\begin{bmatrix}
5 & 5 & 1.5 & 1.5 \\
1 & 4.5 & 1 & 4.5
\end{bmatrix}
\]
This matrix includes the x-coordinates in the first row and the corresponding y-coordinates in the second row for points A, B, D, and C respectively.
#### Conclusion
Understanding and creating coordinate matrices is essential for properly describing and working with geometric figures on a plane. This specific matrix helps in identifying the exact positioning and relationship between the vertices of the given quadrilateral ABDC.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d0c88f8-9b0e-4a87-ae6c-39dd67e2599b%2Ffc3a33d2-2e56-424e-a104-91f17b159194%2Faytleg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Coordinate Matrices for Quadrilaterals
#### Problem Statement
**Question:** What is the coordinate matrix that describes the following quadrilateral ABDC?
#### Diagram Explanation
The diagram provided displays a rectangle plotted on a Cartesian coordinate system. Each corner of the rectangle is marked with a blue dot and is labeled with the points A, B, C, and D as follows:
- Point A: Located at the bottom-right corner.
- Point B: Located at the top-right corner.
- Point C: Located at the top-left corner.
- Point D: Located at the bottom-left corner.
The coordinates for each point are as follows:
- A (5, 1)
- B (5, 4.5)
- D (1.5, 1)
- C (1.5, 4.5)
#### Coordinate Matrix Description
The coordinate matrix for the quadrilateral ABDC can be represented in the following manner:
\[
\begin{bmatrix}
A_x & B_x & D_x & C_x \\
A_y & B_y & D_y & C_y
\end{bmatrix}
=
\begin{bmatrix}
5 & 5 & 1.5 & 1.5 \\
1 & 4.5 & 1 & 4.5
\end{bmatrix}
\]
This matrix includes the x-coordinates in the first row and the corresponding y-coordinates in the second row for points A, B, D, and C respectively.
#### Conclusion
Understanding and creating coordinate matrices is essential for properly describing and working with geometric figures on a plane. This specific matrix helps in identifying the exact positioning and relationship between the vertices of the given quadrilateral ABDC.
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