Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question

 Calculate the length of each side (round tenths):

**Algebraic Justification and Distance Calculation** 1. **Prove your justification algebraically** 2. **Calculate the length of each side (round to the nearest tenth):** \[ \begin{array}{|c|c|} \hline d_{AB} & d_{AD} \\ \hline d_{DC} & d_{BC} \\ \hline \end{array} \] - The first cell calculates the distance \( d_{AB} \) (side AB). - The second cell calculates the distance \( d_{AD} \) (side AD). - The third cell calculates the distance \( d_{DC} \) (side DC). - The fourth cell calculates the distance \( d_{BC} \) (side BC). Calculations involve finding the distances between the points on a coordinate plane using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Each resulting distance should be rounded to the nearest tenth of a unit.
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Transcribed Image Text:**Algebraic Justification and Distance Calculation** 1. **Prove your justification algebraically** 2. **Calculate the length of each side (round to the nearest tenth):** \[ \begin{array}{|c|c|} \hline d_{AB} & d_{AD} \\ \hline d_{DC} & d_{BC} \\ \hline \end{array} \] - The first cell calculates the distance \( d_{AB} \) (side AB). - The second cell calculates the distance \( d_{AD} \) (side AD). - The third cell calculates the distance \( d_{DC} \) (side DC). - The fourth cell calculates the distance \( d_{BC} \) (side BC). Calculations involve finding the distances between the points on a coordinate plane using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Each resulting distance should be rounded to the nearest tenth of a unit.
### Understanding Graph Coordinates: Parallelogram on the Cartesian Plane #### Description: The image presents a parallelogram plotted on a Cartesian coordinate system. The graph uses a grid to help visualize the points and lines making up the shape. It illustrates a geometric concept using a coordinate system to define the precise location of each vertex of the parallelogram. #### Detailed Explanation: The parallelogram is defined by four vertices A, B, C, and D. These vertices are connected sequentially to form the four sides of the parallelogram. - **Vertices Coordinates**: - Vertex A: Situated at coordinates (-4, 2) - Vertex B: Situated at coordinates (2, 7) - Vertex C: Situated at coordinates (6, 2.5) - Vertex D: Situated at coordinates (0, -3) - **Connecting Lines**: - Line segment AB: Connects vertex A and B. - Line segment BC: Connects vertex B and C. - Line segment CD: Connects vertex C and D. - Line segment DA: Connects vertex D and A. #### Characteristics: - **Parallelism**: Each pair of opposite sides (AB, CD and AD, BC) are equal in length and parallel to each other, a defining property of a parallelogram. - **Axes and Coordinates**: The x-axis and y-axis intersect at the origin (0,0), which acts as a central reference point. The grid lines mark both positive and negative values on the x and y axes, from -10 to 10, convenient for plotting and referencing coordinates. - **Shading**: The inside of the parallelogram is shaded to distinguish the shape clearly from the rest of the grid. This shading helps in visualizing the entire enclosed area formed by the vertices and connecting lines. This graph effectively demonstrates the geometric principle and provides a precise visual aid for understanding how a parallelogram is formed and defined within a coordinate plane using Cartesian coordinates.
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Transcribed Image Text:### Understanding Graph Coordinates: Parallelogram on the Cartesian Plane #### Description: The image presents a parallelogram plotted on a Cartesian coordinate system. The graph uses a grid to help visualize the points and lines making up the shape. It illustrates a geometric concept using a coordinate system to define the precise location of each vertex of the parallelogram. #### Detailed Explanation: The parallelogram is defined by four vertices A, B, C, and D. These vertices are connected sequentially to form the four sides of the parallelogram. - **Vertices Coordinates**: - Vertex A: Situated at coordinates (-4, 2) - Vertex B: Situated at coordinates (2, 7) - Vertex C: Situated at coordinates (6, 2.5) - Vertex D: Situated at coordinates (0, -3) - **Connecting Lines**: - Line segment AB: Connects vertex A and B. - Line segment BC: Connects vertex B and C. - Line segment CD: Connects vertex C and D. - Line segment DA: Connects vertex D and A. #### Characteristics: - **Parallelism**: Each pair of opposite sides (AB, CD and AD, BC) are equal in length and parallel to each other, a defining property of a parallelogram. - **Axes and Coordinates**: The x-axis and y-axis intersect at the origin (0,0), which acts as a central reference point. The grid lines mark both positive and negative values on the x and y axes, from -10 to 10, convenient for plotting and referencing coordinates. - **Shading**: The inside of the parallelogram is shaded to distinguish the shape clearly from the rest of the grid. This shading helps in visualizing the entire enclosed area formed by the vertices and connecting lines. This graph effectively demonstrates the geometric principle and provides a precise visual aid for understanding how a parallelogram is formed and defined within a coordinate plane using Cartesian coordinates.
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