At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Certainly! Let's walk through the process of translating each given ordered pair by the translation vector [tex]\( T(4, -3) \)[/tex].
### Explanation of Translation:
A translation moves every point of a figure or a space by the same amount in a given direction. In coordinate geometry, if you want to translate a point [tex]\((x, y)\)[/tex] by a vector [tex]\( (a, b) \)[/tex], you add [tex]\( a \)[/tex] to the [tex]\( x \)[/tex]-coordinate and [tex]\( b \)[/tex] to the [tex]\( y \)[/tex]-coordinate. This means the translated point will be [tex]\((x + a, y + b)\)[/tex].
For this problem, the translation vector given is [tex]\( (4, -3) \)[/tex]. This means we will add 4 to the x-coordinate and subtract 3 from the y-coordinate for each pair.
### Given Ordered Pairs and Translation Process:
1. Original Pair: [tex]\( (-9, 2) \)[/tex]
- Translated X-coordinate: [tex]\( -9 + 4 = -5 \)[/tex]
- Translated Y-coordinate: [tex]\( 2 - 3 = -1 \)[/tex]
- Translated Pair: [tex]\( (-5, -1) \)[/tex]
2. Original Pair: [tex]\( (0, -5) \)[/tex]
- Translated X-coordinate: [tex]\( 0 + 4 = 4 \)[/tex]
- Translated Y-coordinate: [tex]\( -5 - 3 = -8 \)[/tex]
- Translated Pair: [tex]\( (4, -8) \)[/tex]
3. Original Pair: [tex]\( (-5, -1) \)[/tex]
- Translated X-coordinate: [tex]\( -5 + 4 = -1 \)[/tex]
- Translated Y-coordinate: [tex]\( -1 - 3 = -4 \)[/tex]
- Translated Pair: [tex]\( (-1, -4) \)[/tex]
4. Original Pair: [tex]\( (12, 5) \)[/tex]
- Translated X-coordinate: [tex]\( 12 + 4 = 16 \)[/tex]
- Translated Y-coordinate: [tex]\( 5 - 3 = 2 \)[/tex]
- Translated Pair: [tex]\( (16, 2) \)[/tex]
5. Original Pair: [tex]\( (-5, -1) \)[/tex] (repeated)
- Translated X-coordinate: [tex]\( -5 + 4 = -1 \)[/tex]
- Translated Y-coordinate: [tex]\( -1 - 3 = -4 \)[/tex]
- Translated Pair: [tex]\( (-1, -4) \)[/tex] (same as before)
6. Original Pair: [tex]\( (4, -8) \)[/tex]
- Translated X-coordinate: [tex]\( 4 + 4 = 8 \)[/tex]
- Translated Y-coordinate: [tex]\( -8 - 3 = -11 \)[/tex]
- Translated Pair: [tex]\( (8, -11) \)[/tex]
7. Original Pair: [tex]\( (5, 2) \)[/tex]
- Translated X-coordinate: [tex]\( 5 + 4 = 9 \)[/tex]
- Translated Y-coordinate: [tex]\( 2 - 3 = -1 \)[/tex]
- Translated Pair: [tex]\( (9, -1) \)[/tex]
8. Original Pair: [tex]\( (6, 9) \)[/tex]
- Translated X-coordinate: [tex]\( 6 + 4 = 10 \)[/tex]
- Translated Y-coordinate: [tex]\( 9 - 3 = 6 \)[/tex]
- Translated Pair: [tex]\( (10, 6) \)[/tex]
9. Original Pair: [tex]\( (5, -2) \)[/tex]
- Translated X-coordinate: [tex]\( 5 + 4 = 9 \)[/tex]
- Translated Y-coordinate: [tex]\( -2 - 3 = -5 \)[/tex]
- Translated Pair: [tex]\( (9, -5) \)[/tex]
10. Original Pair: [tex]\( (1, 1) \)[/tex]
- Translated X-coordinate: [tex]\( 1 + 4 = 5 \)[/tex]
- Translated Y-coordinate: [tex]\( 1 - 3 = -2 \)[/tex]
- Translated Pair: [tex]\( (5, -2) \)[/tex]
### Summary of Translated Pairs:
After applying the translation [tex]\( T(4, -3) \)[/tex] to each given pair, the resulting translated pairs are:
[tex]\[ (-5, -1), (4, -8), (-1, -4), (16, 2), (-1, -4), (8, -11), (9, -1), (10, 6), (9, -5), (5, -2) \][/tex]
These are the new coordinates of the points after the translation.
### Explanation of Translation:
A translation moves every point of a figure or a space by the same amount in a given direction. In coordinate geometry, if you want to translate a point [tex]\((x, y)\)[/tex] by a vector [tex]\( (a, b) \)[/tex], you add [tex]\( a \)[/tex] to the [tex]\( x \)[/tex]-coordinate and [tex]\( b \)[/tex] to the [tex]\( y \)[/tex]-coordinate. This means the translated point will be [tex]\((x + a, y + b)\)[/tex].
For this problem, the translation vector given is [tex]\( (4, -3) \)[/tex]. This means we will add 4 to the x-coordinate and subtract 3 from the y-coordinate for each pair.
### Given Ordered Pairs and Translation Process:
1. Original Pair: [tex]\( (-9, 2) \)[/tex]
- Translated X-coordinate: [tex]\( -9 + 4 = -5 \)[/tex]
- Translated Y-coordinate: [tex]\( 2 - 3 = -1 \)[/tex]
- Translated Pair: [tex]\( (-5, -1) \)[/tex]
2. Original Pair: [tex]\( (0, -5) \)[/tex]
- Translated X-coordinate: [tex]\( 0 + 4 = 4 \)[/tex]
- Translated Y-coordinate: [tex]\( -5 - 3 = -8 \)[/tex]
- Translated Pair: [tex]\( (4, -8) \)[/tex]
3. Original Pair: [tex]\( (-5, -1) \)[/tex]
- Translated X-coordinate: [tex]\( -5 + 4 = -1 \)[/tex]
- Translated Y-coordinate: [tex]\( -1 - 3 = -4 \)[/tex]
- Translated Pair: [tex]\( (-1, -4) \)[/tex]
4. Original Pair: [tex]\( (12, 5) \)[/tex]
- Translated X-coordinate: [tex]\( 12 + 4 = 16 \)[/tex]
- Translated Y-coordinate: [tex]\( 5 - 3 = 2 \)[/tex]
- Translated Pair: [tex]\( (16, 2) \)[/tex]
5. Original Pair: [tex]\( (-5, -1) \)[/tex] (repeated)
- Translated X-coordinate: [tex]\( -5 + 4 = -1 \)[/tex]
- Translated Y-coordinate: [tex]\( -1 - 3 = -4 \)[/tex]
- Translated Pair: [tex]\( (-1, -4) \)[/tex] (same as before)
6. Original Pair: [tex]\( (4, -8) \)[/tex]
- Translated X-coordinate: [tex]\( 4 + 4 = 8 \)[/tex]
- Translated Y-coordinate: [tex]\( -8 - 3 = -11 \)[/tex]
- Translated Pair: [tex]\( (8, -11) \)[/tex]
7. Original Pair: [tex]\( (5, 2) \)[/tex]
- Translated X-coordinate: [tex]\( 5 + 4 = 9 \)[/tex]
- Translated Y-coordinate: [tex]\( 2 - 3 = -1 \)[/tex]
- Translated Pair: [tex]\( (9, -1) \)[/tex]
8. Original Pair: [tex]\( (6, 9) \)[/tex]
- Translated X-coordinate: [tex]\( 6 + 4 = 10 \)[/tex]
- Translated Y-coordinate: [tex]\( 9 - 3 = 6 \)[/tex]
- Translated Pair: [tex]\( (10, 6) \)[/tex]
9. Original Pair: [tex]\( (5, -2) \)[/tex]
- Translated X-coordinate: [tex]\( 5 + 4 = 9 \)[/tex]
- Translated Y-coordinate: [tex]\( -2 - 3 = -5 \)[/tex]
- Translated Pair: [tex]\( (9, -5) \)[/tex]
10. Original Pair: [tex]\( (1, 1) \)[/tex]
- Translated X-coordinate: [tex]\( 1 + 4 = 5 \)[/tex]
- Translated Y-coordinate: [tex]\( 1 - 3 = -2 \)[/tex]
- Translated Pair: [tex]\( (5, -2) \)[/tex]
### Summary of Translated Pairs:
After applying the translation [tex]\( T(4, -3) \)[/tex] to each given pair, the resulting translated pairs are:
[tex]\[ (-5, -1), (4, -8), (-1, -4), (16, 2), (-1, -4), (8, -11), (9, -1), (10, 6), (9, -5), (5, -2) \][/tex]
These are the new coordinates of the points after the translation.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
