Rectangle EFGH Is Translated According To The Rule T − 5 , 9 ( X , Y T_{-5,9}(x, Y T − 5 , 9 ​ ( X , Y ]. If The Coordinates Of The Pre-image Of Point H Are ( − 2 , − 3 (-2, -3 ( − 2 , − 3 ], What Are The Coordinates Of H ′ H' H ′ ?A. ( 7 , − 9 (7, -9 ( 7 , − 9 ] B. ( − 7 , 6 (-7, 6 ( − 7 , 6 ] C. $(3,

Translation is a fundamental concept in geometry that involves moving a figure from one location to another without changing its size or shape. In this article, we will explore the concept of translation and how it applies to the given problem involving a rectangle.

What is Translation?

Translation is a transformation that moves a figure from one location to another without changing its size or shape. It is a type of rigid motion that preserves the properties of the figure, such as its shape, size, and orientation. Translation can be represented by a vector, which indicates the direction and magnitude of the movement.

The Translation Rule

In the given problem, the translation rule is $T_{-5,9}(x, y)$. This means that the translation involves moving the figure 5 units to the left and 9 units up. The translation rule can be represented by the vector $(-5, 9)$, which indicates the direction and magnitude of the movement.

Applying the Translation Rule

To apply the translation rule, we need to add the corresponding components of the translation vector to the coordinates of the pre-image point. In this case, the pre-image point is $H(-2, -3)$. To find the coordinates of $H'$, we need to add the components of the translation vector to the coordinates of $H$.

Calculating the Coordinates of $H'$

To calculate the coordinates of $H'$, we need to add the corresponding components of the translation vector to the coordinates of $H$. The translation vector is $(-5, 9)$, so we need to add $-5$ to the x-coordinate and $9$ to the y-coordinate of $H$.

x = -2 + (-5)
y = -3 + 9

Simplifying the Expressions

To simplify the expressions, we can evaluate the arithmetic operations.

x = -7
y = 6

Conclusion

In conclusion, the coordinates of $H'$ are $(-7, 6)$. This is the result of applying the translation rule $T_{-5,9}(x, y)$ to the pre-image point $H(-2, -3)$.

Discussion

The given problem involves a translation of a rectangle according to the rule $T_{-5,9}(x, y)$. The pre-image point is $H(-2, -3)$, and we need to find the coordinates of $H'$. To solve this problem, we need to apply the translation rule by adding the corresponding components of the translation vector to the coordinates of the pre-image point.

Key Takeaways

• Translation is a fundamental concept in geometry that involves moving a figure from one location to another without changing its size or shape.
• The translation rule can be represented by a vector, which indicates the direction and magnitude of the movement.
• To apply the translation rule, we need to add the corresponding components of the translation vector to the coordinates of the pre-image point.
• The coordinates of $H'$ can be found by adding the components of the translation vector to the coordinates of $H$.

Practice Problems

1. A rectangle is translated according to the rule $T_{3,4}(x, y)$. If the coordinates of the pre-image of point $H$ are $(2, 1)$, what are the coordinates of $H'$?
2. A triangle is translated according to the rule $T_{-2,5}(x, y)$. If the coordinates of the pre-image of point $H$ are $(-1, 2)$, what are the coordinates of $H'$?

Answer Key

1. $(5, 5)$
2. $(-3, 7)$
   Rectangle EFGH Translation Q&A =====================================

Q: What is the definition of translation in geometry?

A: Translation is a fundamental concept in geometry that involves moving a figure from one location to another without changing its size or shape. It is a type of rigid motion that preserves the properties of the figure, such as its shape, size, and orientation.

Q: How is the translation rule represented?

A: The translation rule can be represented by a vector, which indicates the direction and magnitude of the movement. In the given problem, the translation rule is $T_{-5,9}(x, y)$, which means that the translation involves moving the figure 5 units to the left and 9 units up.

Q: How do you apply the translation rule to find the coordinates of $H'$?

A: To apply the translation rule, you need to add the corresponding components of the translation vector to the coordinates of the pre-image point. In this case, the pre-image point is $H(-2, -3)$. To find the coordinates of $H'$, you need to add the components of the translation vector to the coordinates of $H$.

Q: What are the coordinates of $H'$?

A: The coordinates of $H'$ are $(-7, 6)$. This is the result of applying the translation rule $T_{-5,9}(x, y)$ to the pre-image point $H(-2, -3)$.

Q: What is the difference between translation and rotation?

A: Translation and rotation are both types of rigid motions, but they differ in the way they move the figure. Translation involves moving the figure from one location to another without changing its size or shape, while rotation involves rotating the figure around a fixed point without changing its size or shape.

Q: Can you provide an example of a translation problem?

A: Yes, here's an example:

A rectangle is translated according to the rule $T_{3,4}(x, y)$. If the coordinates of the pre-image of point $H$ are $(2, 1)$, what are the coordinates of $H'$?

To solve this problem, you need to apply the translation rule by adding the corresponding components of the translation vector to the coordinates of the pre-image point.

Q: How do you determine the direction and magnitude of the translation vector?

A: The direction and magnitude of the translation vector can be determined by the components of the translation rule. In the given problem, the translation rule is $T_{-5,9}(x, y)$, which means that the translation involves moving the figure 5 units to the left and 9 units up.

Q: Can you provide a real-world example of translation?

A: Yes, here's a real-world example:

Imagine you are moving a piece of furniture from one room to another. You need to move the furniture from its original location to a new location without changing its size or shape. This is an example of translation, where you are moving the furniture from one location to another without changing its size or shape.

Q: How do you represent the translation rule in a mathematical equation?

A: The translation rule can be represented by a mathematical equation, such as:

$T_{a,b}(x, y) = (x + a, y + b)$

where $(x, y)$ is the pre-image point, and $(a, b)$ is the translation vector.

Q: Can you provide a summary of the key takeaways from this article?

A: Yes, here's a summary of the key takeaways:

• Translation is a fundamental concept in geometry that involves moving a figure from one location to another without changing its size or shape.
• The translation rule can be represented by a vector, which indicates the direction and magnitude of the movement.
• To apply the translation rule, you need to add the corresponding components of the translation vector to the coordinates of the pre-image point.
• The coordinates of $H'$ can be found by adding the components of the translation vector to the coordinates of $H$.

Practice Problems

1. A rectangle is translated according to the rule $T_{2,3}(x, y)$. If the coordinates of the pre-image of point $H$ are $(4, 2)$, what are the coordinates of $H'$?
2. A triangle is translated according to the rule $T_{-1,4}(x, y)$. If the coordinates of the pre-image of point $H$ are $(-3, 1)$, what are the coordinates of $H'$?

Answer Key

1. $(6, 5)$
2. $(-4, 5)$