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Answer :
To solve this question about the translation of a rhombus, let’s break down what each statement means and what happens during a translation:
1. Understanding Translations:
- A translation is a type of transformation that slides a figure in a straight line from one position to another without rotating it or changing its size.
2. Effect on a Rhombus:
- A rhombus is a quadrilateral with all sides of equal length and opposite angles that are equal.
- When a figure like a rhombus is translated, its position changes, but its shape, size, and angle measures remain the same.
Now, let's look at each option:
A. The sides of the rhombus will decrease in length 5 units.
- This is incorrect because a translation does not change the length of the sides; it only moves the figure without altering its dimensions.
B. The angles of the rhombus will decrease in measure of 5 degrees.
- This is incorrect because a translation does not affect the angle measures in any way. Angles remain the same during translation.
C. The location of the vertices of the rhombus will not change because of the translation.
- This is incorrect because the definition of translation is to move the shape. Hence, the vertices will change their location.
D. The angle measures of the rhombus will not change because of the translation.
- This is correct. As mentioned before, translations do not change the size, shape, or angle measures of a figure. The angle measures will remain the same.
In conclusion, the statement that must be true after translating Rhombus WXYZ 5 units down is:
D. The angle measures of the rhombus will not change because of the translation.
1. Understanding Translations:
- A translation is a type of transformation that slides a figure in a straight line from one position to another without rotating it or changing its size.
2. Effect on a Rhombus:
- A rhombus is a quadrilateral with all sides of equal length and opposite angles that are equal.
- When a figure like a rhombus is translated, its position changes, but its shape, size, and angle measures remain the same.
Now, let's look at each option:
A. The sides of the rhombus will decrease in length 5 units.
- This is incorrect because a translation does not change the length of the sides; it only moves the figure without altering its dimensions.
B. The angles of the rhombus will decrease in measure of 5 degrees.
- This is incorrect because a translation does not affect the angle measures in any way. Angles remain the same during translation.
C. The location of the vertices of the rhombus will not change because of the translation.
- This is incorrect because the definition of translation is to move the shape. Hence, the vertices will change their location.
D. The angle measures of the rhombus will not change because of the translation.
- This is correct. As mentioned before, translations do not change the size, shape, or angle measures of a figure. The angle measures will remain the same.
In conclusion, the statement that must be true after translating Rhombus WXYZ 5 units down is:
D. The angle measures of the rhombus will not change because of the translation.
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