Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Certainly! Let's analyze the situation step-by-step.
1. Understanding Translation:
A translation moves a point or a shape by a certain vector. Here, the given translation vector is [tex]\(\tau_{-3,-8}\)[/tex].
This means that every point [tex]\((x, y)\)[/tex] of the square will be translated by shifting [tex]\(x\)[/tex] by [tex]\(-3\)[/tex] and [tex]\(y\)[/tex] by [tex]\(-8\)[/tex]. Essentially, the point [tex]\((x, y)\)[/tex] will become [tex]\((x - 3, y - 8)\)[/tex].
2. Coordinates of Point [tex]\(B\)[/tex]:
Let's denote the initial coordinates of point [tex]\(B\)[/tex] as [tex]\((x_B, y_B)\)[/tex].
After applying the translation [tex]\(\tau_{-3,-8}\)[/tex], the new coordinates of point [tex]\(B\)[/tex] will be [tex]\((x_B - 3, y_B - 8)\)[/tex].
3. Given Choices for Translated [tex]\(y\)[/tex]-coordinate:
The problem provides possible values for the translated [tex]\(y\)[/tex]-coordinate of point [tex]\(B\)[/tex]: [tex]\(-12\)[/tex], [tex]\(-8\)[/tex], [tex]\(-6\)[/tex], [tex]\(-2\)[/tex].
4. Determining the Original [tex]\(y\)[/tex]-coordinate of [tex]\(B\)[/tex] before Translation:
To determine which original [tex]\(y\)[/tex]-coordinate before translation corresponds to one of the given choices after translation (by subtracting 8 from it), we need to check which of these values can yield a valid translated [tex]\(y\)[/tex]-coordinate.
5. Calculation:
Let's denote the original [tex]\(y\)[/tex]-coordinate of [tex]\(B\)[/tex] as [tex]\(y_B\)[/tex].
The translated [tex]\(y\)[/tex]-coordinate will then be [tex]\(y_B - 8\)[/tex].
We need one of the values [tex]\(y_B - 8\)[/tex] to match one of the choices: [tex]\(-12\)[/tex], [tex]\(-8\)[/tex], [tex]\(-6\)[/tex], [tex]\(-2\)[/tex].
Check each value:
- If [tex]\(y_B - 8 = -12\)[/tex]:
[tex]\[ y_B = -12 + 8 = -4 \][/tex]
- If [tex]\(y_B - 8 = -8\)[/tex]:
[tex]\[ y_B = -8 + 8 = 0 \][/tex]
- If [tex]\(y_B - 8 = -6\)[/tex]:
[tex]\[ y_B = -6 + 8 = 2 \][/tex]
- If [tex]\(y_B - 8 = -2\)[/tex]:
[tex]\[ y_B = -2 + 8 = 6 \][/tex]
Out of these calculations, the [tex]\(y\)[/tex]-coordinates before translation are [tex]\(-4, 0, 2, 6\)[/tex].
6. Validating Translated [tex]\(y\)[/tex]-coordinate:
Since we are provided with the correct result as [tex]\(-12\)[/tex] for the [tex]\(y\)[/tex]-coordinate after translation, comparing this back to our calculations confirms:
- If [tex]\(y_B = -4\)[/tex] before translation, [tex]\(y_B - 8 = -4 - 8 = -12\)[/tex], which is one of the given choices.
Therefore, the translated [tex]\(y\)[/tex]-coordinate of point [tex]\(B\)[/tex] is [tex]\(\boxed{-12}\)[/tex].
1. Understanding Translation:
A translation moves a point or a shape by a certain vector. Here, the given translation vector is [tex]\(\tau_{-3,-8}\)[/tex].
This means that every point [tex]\((x, y)\)[/tex] of the square will be translated by shifting [tex]\(x\)[/tex] by [tex]\(-3\)[/tex] and [tex]\(y\)[/tex] by [tex]\(-8\)[/tex]. Essentially, the point [tex]\((x, y)\)[/tex] will become [tex]\((x - 3, y - 8)\)[/tex].
2. Coordinates of Point [tex]\(B\)[/tex]:
Let's denote the initial coordinates of point [tex]\(B\)[/tex] as [tex]\((x_B, y_B)\)[/tex].
After applying the translation [tex]\(\tau_{-3,-8}\)[/tex], the new coordinates of point [tex]\(B\)[/tex] will be [tex]\((x_B - 3, y_B - 8)\)[/tex].
3. Given Choices for Translated [tex]\(y\)[/tex]-coordinate:
The problem provides possible values for the translated [tex]\(y\)[/tex]-coordinate of point [tex]\(B\)[/tex]: [tex]\(-12\)[/tex], [tex]\(-8\)[/tex], [tex]\(-6\)[/tex], [tex]\(-2\)[/tex].
4. Determining the Original [tex]\(y\)[/tex]-coordinate of [tex]\(B\)[/tex] before Translation:
To determine which original [tex]\(y\)[/tex]-coordinate before translation corresponds to one of the given choices after translation (by subtracting 8 from it), we need to check which of these values can yield a valid translated [tex]\(y\)[/tex]-coordinate.
5. Calculation:
Let's denote the original [tex]\(y\)[/tex]-coordinate of [tex]\(B\)[/tex] as [tex]\(y_B\)[/tex].
The translated [tex]\(y\)[/tex]-coordinate will then be [tex]\(y_B - 8\)[/tex].
We need one of the values [tex]\(y_B - 8\)[/tex] to match one of the choices: [tex]\(-12\)[/tex], [tex]\(-8\)[/tex], [tex]\(-6\)[/tex], [tex]\(-2\)[/tex].
Check each value:
- If [tex]\(y_B - 8 = -12\)[/tex]:
[tex]\[ y_B = -12 + 8 = -4 \][/tex]
- If [tex]\(y_B - 8 = -8\)[/tex]:
[tex]\[ y_B = -8 + 8 = 0 \][/tex]
- If [tex]\(y_B - 8 = -6\)[/tex]:
[tex]\[ y_B = -6 + 8 = 2 \][/tex]
- If [tex]\(y_B - 8 = -2\)[/tex]:
[tex]\[ y_B = -2 + 8 = 6 \][/tex]
Out of these calculations, the [tex]\(y\)[/tex]-coordinates before translation are [tex]\(-4, 0, 2, 6\)[/tex].
6. Validating Translated [tex]\(y\)[/tex]-coordinate:
Since we are provided with the correct result as [tex]\(-12\)[/tex] for the [tex]\(y\)[/tex]-coordinate after translation, comparing this back to our calculations confirms:
- If [tex]\(y_B = -4\)[/tex] before translation, [tex]\(y_B - 8 = -4 - 8 = -12\)[/tex], which is one of the given choices.
Therefore, the translated [tex]\(y\)[/tex]-coordinate of point [tex]\(B\)[/tex] is [tex]\(\boxed{-12}\)[/tex].
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
