25. Two quadrilaterals are shown on the coordinate grid: 10 8. 6 2 10 -8 -6 -4 -2 4 6 8 10 -2 -4 -6 W -8 -10 Stephan can map quadrilateral JKLM onto quadrilateral WXYZ with a reflection across the x-axis followed by a translation 3 units down and 2 units to the right. Which statement best describes the congruence of the two quadrilaterals? A. They are not congruent because translations preserve length but reflections do not. B. They are not congruent because reflections preserve length but translations do not. C. They are not congruent because neither reflections nor translations preserve length. D. They are congruent because both reflections and translations preserve length. N of 으

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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Question 25

### Question 25: Congruence of Quadrilaterals on a Coordinate Grid

#### Description:
Two quadrilaterals are illustrated on a coordinate grid. Quadrilateral \(JKLM\) is labeled with vertices \(J\), \(K\), \(L\), and \(M\), while quadrilateral \(WXYZ\) is labeled with vertices \(W\), \(X\), \(Y\), and \(Z\).

#### Graph Details:
- The graph displays a standard Cartesian coordinate system with both the x-axis and y-axis ranging from -10 to 10.
- The quadrilateral \(JKLM\) is positioned in the upper right quadrant of the graph.
   - \(J (2, 3)\)
   - \(K (4, 6)\)
   - \(L (5, 2)\)
   - \(M (3, 0)\)
- The quadrilateral \(WXYZ\) is positioned in the lower right quadrant of the graph.
   - \(W (3, -2)\)
   - \(X (5, -5)\)
   - \(Y (6, -1)\)
   - \(Z (4, 1)\)

#### Transformation Explanation:
Stephan can map quadrilateral \(JKLM\) onto quadrilateral \(WXYZ\) with a reflection across the x-axis followed by a translation of 3 units down and 2 units to the right.

#### Question:
Which statement best describes the congruence of the two quadrilaterals?
- **A.** They are not congruent because translations preserve length but reflections do not.
- **B.** They are not congruent because reflections preserve length but translations do not.
- **C.** They are not congruent because neither reflections nor translations preserve length.
- **D.** They are congruent because both reflections and translations preserve length. 

**Answer:**
- **Correct Answer: D.** They are congruent because both reflections and translations preserve length.

#### Explanation:
Reflections and translations are rigid transformations, which means they preserve the lengths of segments and the measures of angles. Therefore, the quadrilateral \(JKLM\) and quadrilateral \(WXYZ\) are congruent.
Transcribed Image Text:### Question 25: Congruence of Quadrilaterals on a Coordinate Grid #### Description: Two quadrilaterals are illustrated on a coordinate grid. Quadrilateral \(JKLM\) is labeled with vertices \(J\), \(K\), \(L\), and \(M\), while quadrilateral \(WXYZ\) is labeled with vertices \(W\), \(X\), \(Y\), and \(Z\). #### Graph Details: - The graph displays a standard Cartesian coordinate system with both the x-axis and y-axis ranging from -10 to 10. - The quadrilateral \(JKLM\) is positioned in the upper right quadrant of the graph. - \(J (2, 3)\) - \(K (4, 6)\) - \(L (5, 2)\) - \(M (3, 0)\) - The quadrilateral \(WXYZ\) is positioned in the lower right quadrant of the graph. - \(W (3, -2)\) - \(X (5, -5)\) - \(Y (6, -1)\) - \(Z (4, 1)\) #### Transformation Explanation: Stephan can map quadrilateral \(JKLM\) onto quadrilateral \(WXYZ\) with a reflection across the x-axis followed by a translation of 3 units down and 2 units to the right. #### Question: Which statement best describes the congruence of the two quadrilaterals? - **A.** They are not congruent because translations preserve length but reflections do not. - **B.** They are not congruent because reflections preserve length but translations do not. - **C.** They are not congruent because neither reflections nor translations preserve length. - **D.** They are congruent because both reflections and translations preserve length. **Answer:** - **Correct Answer: D.** They are congruent because both reflections and translations preserve length. #### Explanation: Reflections and translations are rigid transformations, which means they preserve the lengths of segments and the measures of angles. Therefore, the quadrilateral \(JKLM\) and quadrilateral \(WXYZ\) are congruent.
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