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Quadrilateral A'B'C'D' is the Image of quadrilateral ABCD under a translation. 6- -6-5-4-3-2Y 2 34567 -3, D-7 బాి ి

Quadrilateral A'B'C'D' is the Image of quadrilateral ABCD under a translation. 6- -6-5-4-3-2Y 2 34567 -3, D-7 బాి ి

Elementary Geometry For College Students, 7e
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
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**Determine Translations** Quadrilateral \( A'B'C'D' \) is the image of quadrilateral \( ABCD \) under a translation. [Image Description: The image shows a graph with labeled quadrilaterals. Quadrilateral \( ABCD \) is in blue, and quadrilateral \( A'B'C'D' \) is in red. Each quadrilateral has four vertices marked with their respective points.] **Graph Explanation:** - The x-axis and y-axis are labeled with each interval representing one unit. - Points \( A, B, C, \) and \( D \) are the vertices of quadrilateral \( ABCD \): - \( A(0, 1) \) - \( B(1, 5) \) - \( C(4, 3) \) - \( D(2, 1) \) - Points \( A', B', C', \) and \( D' \) are the vertices of quadrilateral \( A'B'C'D' \), the translated image of \( ABCD \): - \( A'(4, 5) \) - \( B'(5, 9) \) - \( C'(8, 7) \) - \( D'(6, 5) \) **Task**: Determine the translation. *Use non-negative numbers.* To solve the translation, determine how each point of quadrilateral \( ABCD \) moved to its corresponding point in quadrilateral \( A'B'C'D' \). This can be achieved by subtracting the coordinates of \( ABCD \) from \( A'B'C'D' \), respectively. Based on the coordinates: - \( A \) to \( A' \): - \( (0 + 4, 1 + 4) \rightarrow (4, 5) \) - \( B \) to \( B' \): - \( (1 + 4, 5 + 4) \rightarrow (5, 9) \) - \( C \) to \( C' \): - \( (4 + 4, 3 + 4) \rightarrow (8, 7) \) - \( D \) to \( D' \): - \( (2 + 4, 1 + 4) \rightarrow (6, 5) \) Thus, the translation is
Transcribed Image Text:**Determine Translations** Quadrilateral \( A'B'C'D' \) is the image of quadrilateral \( ABCD \) under a translation. [Image Description: The image shows a graph with labeled quadrilaterals. Quadrilateral \( ABCD \) is in blue, and quadrilateral \( A'B'C'D' \) is in red. Each quadrilateral has four vertices marked with their respective points.] **Graph Explanation:** - The x-axis and y-axis are labeled with each interval representing one unit. - Points \( A, B, C, \) and \( D \) are the vertices of quadrilateral \( ABCD \): - \( A(0, 1) \) - \( B(1, 5) \) - \( C(4, 3) \) - \( D(2, 1) \) - Points \( A', B', C', \) and \( D' \) are the vertices of quadrilateral \( A'B'C'D' \), the translated image of \( ABCD \): - \( A'(4, 5) \) - \( B'(5, 9) \) - \( C'(8, 7) \) - \( D'(6, 5) \) **Task**: Determine the translation. *Use non-negative numbers.* To solve the translation, determine how each point of quadrilateral \( ABCD \) moved to its corresponding point in quadrilateral \( A'B'C'D' \). This can be achieved by subtracting the coordinates of \( ABCD \) from \( A'B'C'D' \), respectively. Based on the coordinates: - \( A \) to \( A' \): - \( (0 + 4, 1 + 4) \rightarrow (4, 5) \) - \( B \) to \( B' \): - \( (1 + 4, 5 + 4) \rightarrow (5, 9) \) - \( C \) to \( C' \): - \( (4 + 4, 3 + 4) \rightarrow (8, 7) \) - \( D \) to \( D' \): - \( (2 + 4, 1 + 4) \rightarrow (6, 5) \) Thus, the translation is
**Understanding Translations in Geometry** When working with transformations in geometry, one important type of transformation to understand is translation. A translation is a type of transformation that slides each point of a shape or figure the same distance in the same direction. This transformation moves the shape on a coordinate plane without changing its orientation or size. In the text input box, you are asked to specify: - The number of units for the translation. - The direction of the translation (right, left, up, or down). Here is how you specify a translation: - Enter the desired number of units in the input field. - Choose the appropriate direction from the dropdown menu options: right, left, up, or down. By completing these steps, you effectively define how the shape will be translated on the coordinate plane. Remember: - Translating a shape "right" means adding the specified units to the x-coordinates of all the points of the shape. - Translating a shape "left" means subtracting the specified units from the x-coordinates of all the points of the shape. - Translating a shape "up" means adding the specified units to the y-coordinates of all the points of the shape. - Translating a shape "down" means subtracting the specified units from the y-coordinates of all the points of the shape. **Example:** If you have a point at (3, 4) and you translate it by 2 units to the right, the new coordinates will be (5, 4). If you translate the same point by 2 units down, the new coordinates will be (3, 2). By understanding and using translations effectively, you can manipulate and transform shapes within a coordinate system, aiding in a wide range of geometric applications.
Transcribed Image Text:**Understanding Translations in Geometry** When working with transformations in geometry, one important type of transformation to understand is translation. A translation is a type of transformation that slides each point of a shape or figure the same distance in the same direction. This transformation moves the shape on a coordinate plane without changing its orientation or size. In the text input box, you are asked to specify: - The number of units for the translation. - The direction of the translation (right, left, up, or down). Here is how you specify a translation: - Enter the desired number of units in the input field. - Choose the appropriate direction from the dropdown menu options: right, left, up, or down. By completing these steps, you effectively define how the shape will be translated on the coordinate plane. Remember: - Translating a shape "right" means adding the specified units to the x-coordinates of all the points of the shape. - Translating a shape "left" means subtracting the specified units from the x-coordinates of all the points of the shape. - Translating a shape "up" means adding the specified units to the y-coordinates of all the points of the shape. - Translating a shape "down" means subtracting the specified units from the y-coordinates of all the points of the shape. **Example:** If you have a point at (3, 4) and you translate it by 2 units to the right, the new coordinates will be (5, 4). If you translate the same point by 2 units down, the new coordinates will be (3, 2). By understanding and using translations effectively, you can manipulate and transform shapes within a coordinate system, aiding in a wide range of geometric applications.
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