The Point P ( 6 , − 1 P(6, -1 P ( 6 , − 1 ] Is Translated According To The Rule ( X , Y ) → ( X − 5 , Y − 2 (x, Y) \rightarrow (x-5, Y-2 ( X , Y ) → ( X − 5 , Y − 2 ]. What Are The Coordinates Of P ′ P^{\prime} P ′ ?A. P ′ ( 1 , 2 P^{\prime}(1, 2 P ′ ( 1 , 2 ] B. P ′ ( 1 , 1 P^{\prime}(1, 1 P ′ ( 1 , 1 ] C. $P^{\prime}(1,

Understanding the Translation Rule

In mathematics, a translation is a fundamental concept in geometry that involves moving a point or a shape from one location to another without changing its size or orientation. The translation rule is a mathematical formula that describes how to move a point from its original position to a new position. In this article, we will explore the translation rule and apply it to find the coordinates of a point $P$ after it has been translated according to a given rule.

The Translation Rule Formula

The translation rule formula is given by:

$$(x, y) \rightarrow (x-h, y-k)$$

where $(x, y)$ are the original coordinates of the point, and $(x-h, y-k)$ are the new coordinates of the point after translation. The values of $h$ and $k$ represent the horizontal and vertical shifts, respectively.

Applying the Translation Rule

In this problem, we are given the point $P(6, -1)$ and the translation rule $(x, y) \rightarrow (x-5, y-2)$. To find the coordinates of $P^{\prime}$, we need to apply the translation rule to the point $P$.

Step 1: Identify the Original Coordinates

The original coordinates of the point $P$ are $(6, -1)$.

Step 2: Identify the Translation Rule

The translation rule is given by $(x, y) \rightarrow (x-5, y-2)$.

Step 3: Apply the Translation Rule

To apply the translation rule, we need to substitute the original coordinates of the point $P$ into the formula:

$$(6, -1) \rightarrow (6-5, -1-2)$$

Step 4: Simplify the Expression

Simplifying the expression, we get:

$$(6-5, -1-2) = (1, -3)$$

Therefore, the coordinates of $P^{\prime}$ are $(1, -3)$.

Conclusion

In this article, we applied the translation rule to find the coordinates of a point $P$ after it has been translated according to a given rule. We identified the original coordinates of the point, the translation rule, and applied the rule to find the new coordinates of the point. The result is the coordinates of $P^{\prime}$, which are $(1, -3)$.

Answer

The correct answer is:

Understanding the Translation Rule

In mathematics, a translation is a fundamental concept in geometry that involves moving a point or a shape from one location to another without changing its size or orientation. The translation rule is a mathematical formula that describes how to move a point from its original position to a new position. In this article, we will explore the translation rule and answer some common questions related to it.

Q: What is the translation rule formula?

A: The translation rule formula is given by:

$$(x, y) \rightarrow (x-h, y-k)$$

where $(x, y)$ are the original coordinates of the point, and $(x-h, y-k)$ are the new coordinates of the point after translation. The values of $h$ and $k$ represent the horizontal and vertical shifts, respectively.

Q: How do I apply the translation rule?

A: To apply the translation rule, you need to substitute the original coordinates of the point into the formula and simplify the expression. For example, if the original coordinates of the point are $(6, -1)$ and the translation rule is $(x, y) \rightarrow (x-5, y-2)$, you would substitute the values into the formula and get:

$$(6, -1) \rightarrow (6-5, -1-2)$$

Simplifying the expression, you get:

$$(6-5, -1-2) = (1, -3)$$

Therefore, the coordinates of $P^{\prime}$ are $(1, -3)$.

Q: What is the difference between a translation and a rotation?

A: A translation is a movement of a point or a shape from one location to another without changing its size or orientation. A rotation, on the other hand, is a movement of a point or a shape around a fixed point or axis, resulting in a change in its orientation.

Q: Can I use the translation rule to move a shape?

A: Yes, you can use the translation rule to move a shape. The translation rule applies to points, but you can also use it to move shapes by applying the rule to each point of the shape.

Q: How do I find the coordinates of a point after a translation?

A: To find the coordinates of a point after a translation, you need to apply the translation rule to the point. This involves substituting the original coordinates of the point into the formula and simplifying the expression.

Q: What are some common applications of the translation rule?

A: The translation rule has many applications in mathematics, science, and engineering. Some common applications include:

• Moving objects in a game or simulation
• Calculating the position of a satellite or a spacecraft
• Designing and building structures, such as bridges or buildings
• Analyzing and solving problems in geometry and trigonometry

Conclusion

In this article, we explored the translation rule and answered some common questions related to it. We discussed the formula for the translation rule, how to apply it, and some common applications of the rule. We hope this article has been helpful in understanding the translation rule and its applications.

Frequently Asked Questions

• Q: What is the translation rule formula? A: The translation rule formula is given by $(x, y) \rightarrow (x-h, y-k)$.
• Q: How do I apply the translation rule? A: To apply the translation rule, you need to substitute the original coordinates of the point into the formula and simplify the expression.
• Q: What is the difference between a translation and a rotation? A: A translation is a movement of a point or a shape from one location to another without changing its size or orientation. A rotation, on the other hand, is a movement of a point or a shape around a fixed point or axis, resulting in a change in its orientation.
• Q: Can I use the translation rule to move a shape? A: Yes, you can use the translation rule to move a shape. The translation rule applies to points, but you can also use it to move shapes by applying the rule to each point of the shape.
• Q: How do I find the coordinates of a point after a translation? A: To find the coordinates of a point after a translation, you need to apply the translation rule to the point. This involves substituting the original coordinates of the point into the formula and simplifying the expression.