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Questions and Answers
Analyze the diagram below and complete the instructions that follow. Triangle has vertices A(-3, -4), B(1, 5), and C(4,1). Is translated so that B' is located at point (-3, 2). State the coordinates of A' and C'.
Analyze the diagram below and complete the instructions that follow. Triangle has vertices A(-3, -4), B(1, 5), and C(4,1). Is translated so that B' is located at point (-3, 2). State the coordinates of A' and C'.
- A'(-4, -3), C'(1, -4)
- A'(1, -1), C'(8, 4)
- A'(-7, -7), C'(0, -2) (correct)
- A'(-6, -8), C'(1, -3)
Write an algebraic rule to describe the translation P(-8, 6) to P'(-10,2).
Write an algebraic rule to describe the translation P(-8, 6) to P'(-10,2).
- Rule B
- Rule A
- Rule D (correct)
- Rule C
Point W(-4, 7) was translated to W'(-2, 4). A student wrote the algebraic rule to describe the translation. Evaluate the student's answer.
Point W(-4, 7) was translated to W'(-2, 4). A student wrote the algebraic rule to describe the translation. Evaluate the student's answer.
- The student's answer is correct.
- Incorrect; add 2 to the x-coordinate and subtract 3 from the y-coordinate. (correct)
- Incorrect; add -4 + -2 to calculate the x-coordinate and add 7 + 4 for the y-coordinate.
- Incorrect; add 3 to the x-coordinate and subtract 2 from the y-coordinate.
Which characteristic does a translation not preserve?
Which characteristic does a translation not preserve?
Analyze the graph below and complete the instructions that follow. Describe the translation in the figure from C to C'.
Analyze the graph below and complete the instructions that follow. Describe the translation in the figure from C to C'.
The endpoints of a segment are (0, -5) and (-3, -7). What are the endpoints of the segment after it has been translated 5 units to the right?
The endpoints of a segment are (0, -5) and (-3, -7). What are the endpoints of the segment after it has been translated 5 units to the right?
The endpoints of a segment are (4, 2) and (-2, 2). What are the endpoints of the segment after it has been translated 6 units down?
The endpoints of a segment are (4, 2) and (-2, 2). What are the endpoints of the segment after it has been translated 6 units down?
Analyze the diagram below and complete the instructions that follow. Triangle has vertices K(1, -4), L(-3, 3), and M(-5, -1). It is translated so that K' is located at point (-3, 2). State the coordinates of L' and M'.
Analyze the diagram below and complete the instructions that follow. Triangle has vertices K(1, -4), L(-3, 3), and M(-5, -1). It is translated so that K' is located at point (-3, 2). State the coordinates of L' and M'.
Pentagon is translated 4 units to the right. One side is 5 cm long. What is the length of the other side after translation?
Pentagon is translated 4 units to the right. One side is 5 cm long. What is the length of the other side after translation?
Write an algebraic rule to describe the translation C(5, -4) to C'(-2, 1).
Write an algebraic rule to describe the translation C(5, -4) to C'(-2, 1).
Use an algebraic rule to describe a translation right 4 units and down 2 units.
Use an algebraic rule to describe a translation right 4 units and down 2 units.
The endpoints of a segment are (4, 2) and (-2, 2). What are the endpoints of the segment after it has been translated 6 units down?
The endpoints of a segment are (4, 2) and (-2, 2). What are the endpoints of the segment after it has been translated 6 units down?
Which characteristic does a translation not preserve?
Which characteristic does a translation not preserve?
Analyze the graph below and complete the instructions that follow. Describe the translation in the figure from A to A'.
Analyze the graph below and complete the instructions that follow. Describe the translation in the figure from A to A'.
Point J(8, 5) was translated to J'(2, 9). A student wrote the algebraic rule to describe the translation. Evaluate the student's answer.
Point J(8, 5) was translated to J'(2, 9). A student wrote the algebraic rule to describe the translation. Evaluate the student's answer.
A triangle has vertices of (-2, -1), (0, -5), and (3, 2). What are the vertices of the image after applying the translation?
A triangle has vertices of (-2, -1), (0, -5), and (3, 2). What are the vertices of the image after applying the translation?
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Study Notes
Translations in Geometry
- Translations involve moving every point of a figure the same distance in a specified direction.
- Examples of translations include moving points by specific coordinate shifts or adjusting distances from the origin.
Analyzing Translations
- For vertices A(-3, -4), B(1, 5), C(4, 1): After translating B to point (-3, 2), the new coordinates for A' and C' are derived based on the translation vector, with options to choose from for the final coordinates.
- Algebraic rules for translations can be established by observing changes in x and y coordinates between original points P and P'.
Characteristics of Translations
- Translations maintain the shape, size, and orientation of the figure but do not preserve the distance from the origin.
- Symmetry properties are preserved, but rotational symmetry may not apply as rotation is a different transformation.
Endpoints and Translations
- The endpoints of line segments can be altered through translations in specific directions, such as moving right or down, which is calculated by adding or subtracting from the original coordinates.
- When translating segments, the change in endpoints is consistent with the prescribed movement (e.g., translating segments 5 units to the right or 6 units down).
Evaluating Translation Rules
- Assessing translated points requires verifying algebraic rules through the correct calculations of adding or subtracting values from the original coordinates.
- Students often make common mistakes in computing new coordinates, especially forgetting to consider the direction of the translation.
Practical Examples
- A triangle with vertices at given coordinates will reflect its new vertices after applying a defined translation.
- Lengths of translated figures remain unchanged, maintaining congruency with the original shapes.
Summary of Key Questions
- Understanding and choosing the correct coordinates after translation requires careful consideration of the initial positioning and the intended movement.
- Multiple-choice questions often test knowledge of translation properties, algebraic descriptions, and the impact on figures.
Visual and Contextual Analysis
- Visual diagrams play a critical role in understanding translations; describing transformations accurately requires attention to both graphical representations and algebraic rules.
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