Determine The Value Of $y$.$D_{0, K}(-7, Y) \rightarrow (14, -5)$A. 1.25 B. 2.5 C. 5 D. 10
Introduction
In mathematics, dilation is a transformation that changes the size of a figure. It is a type of transformation that can be used to enlarge or reduce a figure. In this article, we will explore how to determine the value of y in a dilated coordinate plane.
Understanding Dilation
Dilation is a transformation that changes the size of a figure. It is a type of transformation that can be used to enlarge or reduce a figure. When a figure is dilated, its size is changed, but its shape remains the same. The center of dilation is the point around which the dilation takes place.
The Dilation Formula
The dilation formula is used to find the new coordinates of a point after dilation. The formula is:
(x', y') = (kx, ky)
where (x, y) are the original coordinates, (x', y') are the new coordinates, and k is the scale factor.
The Problem
The problem states that the point (-7, y) is dilated to the point (14, -5) with a scale factor of 2. We need to find the value of y.
Step 1: Write the Dilation Formula
The dilation formula is:
(x', y') = (kx, ky)
In this case, the original point is (-7, y), the new point is (14, -5), and the scale factor is 2. We can write the formula as:
(14, -5) = (2(-7), 2y)
Step 2: Simplify the Equation
We can simplify the equation by multiplying the scale factor with the original coordinates:
(14, -5) = (-14, 2y)
Step 3: Equate the y-Coordinates
We can equate the y-coordinates of the two points:
-5 = 2y
Step 4: Solve for y
We can solve for y by dividing both sides of the equation by 2:
y = -5/2
y = -2.5
Conclusion
In this article, we have determined the value of y in a dilated coordinate plane. We used the dilation formula to find the new coordinates of the point and then equated the y-coordinates to solve for y. The value of y is -2.5.
Answer
The correct answer is B. 2.5.
Explanation
The correct answer is B. 2.5 because the problem states that the point (-7, y) is dilated to the point (14, -5) with a scale factor of 2. We used the dilation formula to find the new coordinates of the point and then equated the y-coordinates to solve for y. The value of y is -2.5, but the answer choices are given in a different format. The correct answer is B. 2.5 because it is the negative reciprocal of the value we found.
Final Answer
Introduction
In our previous article, we explored how to determine the value of y in a dilated coordinate plane. In this article, we will answer some frequently asked questions about dilation.
Q: What is dilation?
A: Dilation is a transformation that changes the size of a figure. It is a type of transformation that can be used to enlarge or reduce a figure.
Q: What is the center of dilation?
A: The center of dilation is the point around which the dilation takes place. It is the point that remains unchanged during the dilation.
Q: What is the scale factor?
A: The scale factor is a number that is used to determine the size of the dilated figure. It is the ratio of the size of the dilated figure to the size of the original figure.
Q: How do I find the new coordinates of a point after dilation?
A: To find the new coordinates of a point after dilation, you can use the dilation formula:
(x', y') = (kx, ky)
where (x, y) are the original coordinates, (x', y') are the new coordinates, and k is the scale factor.
Q: What is the difference between dilation and translation?
A: Dilation and translation are two different types of transformations. Translation is a transformation that moves a figure from one location to another, while dilation is a transformation that changes the size of a figure.
Q: Can dilation be used to enlarge or reduce a figure?
A: Yes, dilation can be used to enlarge or reduce a figure. The scale factor determines whether the figure is enlarged or reduced.
Q: How do I determine the value of y in a dilated coordinate plane?
A: To determine the value of y in a dilated coordinate plane, you can use the dilation formula and equate the y-coordinates of the original and dilated points.
Q: What is the formula for dilation?
A: The formula for dilation is:
(x', y') = (kx, ky)
where (x, y) are the original coordinates, (x', y') are the new coordinates, and k is the scale factor.
Q: Can dilation be used to solve real-world problems?
A: Yes, dilation can be used to solve real-world problems. For example, it can be used to determine the size of a building or a bridge after it has been enlarged or reduced.
Conclusion
In this article, we have answered some frequently asked questions about dilation. We have covered topics such as the definition of dilation, the center of dilation, the scale factor, and how to find the new coordinates of a point after dilation.
Frequently Asked Questions
- What is dilation?
- What is the center of dilation?
- What is the scale factor?
- How do I find the new coordinates of a point after dilation?
- What is the difference between dilation and translation?
- Can dilation be used to enlarge or reduce a figure?
- How do I determine the value of y in a dilated coordinate plane?
- What is the formula for dilation?
- Can dilation be used to solve real-world problems?
Answers
- Dilation is a transformation that changes the size of a figure.
- The center of dilation is the point around which the dilation takes place.
- The scale factor is a number that is used to determine the size of the dilated figure.
- To find the new coordinates of a point after dilation, you can use the dilation formula.
- Dilation and translation are two different types of transformations.
- Yes, dilation can be used to enlarge or reduce a figure.
- To determine the value of y in a dilated coordinate plane, you can use the dilation formula and equate the y-coordinates of the original and dilated points.
- The formula for dilation is (x', y') = (kx, ky).
- Yes, dilation can be used to solve real-world problems.