Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine which ordered pairs could be points on a line parallel to the line containing the points [tex]\((3,4)\)[/tex] and [tex]\((-2,2)\)[/tex], we first need to calculate the slope of the line that passes through [tex]\((3,4)\)[/tex] and [tex]\((-2,2)\)[/tex].
1. Calculate the slope of the line through [tex]\((3,4)\)[/tex] and [tex]\((-2,2)\)[/tex]
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 4}{-2 - 3} = \frac{-2}{-5} = 0.4 \][/tex]
Next, we will calculate the slopes of the lines formed by each pair of points and compare them to the calculated slope [tex]\(0.4\)[/tex]. If the slopes are equal, the lines are parallel.
2. Calculate the slopes for given pairs and compare:
- For [tex]\((-2,-5)\)[/tex] and [tex]\((-7,-3)\)[/tex]:
[tex]\[ \text{slope} = \frac{-3 - (-5)}{-7 - (-2)} = \frac{-3 + 5}{-7 + 2} = \frac{2}{-5} = -0.4 \][/tex]
The slope is [tex]\(-0.4\)[/tex]. This is not equal to [tex]\(0.4\)[/tex], therefore, they are not parallel.
- For [tex]\((-1,1)\)[/tex] and [tex]\((-6,-1)\)[/tex]:
[tex]\[ \text{slope} = \frac{-1 - 1}{-6 - (-1)} = \frac{-1 - 1}{-6 + 1} = \frac{-2}{-5} = 0.4 \][/tex]
The slope is [tex]\(0.4\)[/tex]. This is equal to [tex]\(0.4\)[/tex], therefore, they are parallel.
- For [tex]\((0,0)\)[/tex] and [tex]\((2,5)\)[/tex]:
[tex]\[ \text{slope} = \frac{5 - 0}{2 - 0} = \frac{5}{2} = 2.5 \][/tex]
The slope is [tex]\(2.5\)[/tex]. This is not equal to [tex]\(0.4\)[/tex], therefore, they are not parallel.
- For [tex]\((1,0)\)[/tex] and [tex]\((6,2)\)[/tex]:
[tex]\[ \text{slope} = \frac{2 - 0}{6 - 1} = \frac{2}{5} = 0.4 \][/tex]
The slope is [tex]\(0.4\)[/tex]. This is equal to [tex]\(0.4\)[/tex], therefore, they are parallel.
- For [tex]\((3,0)\)[/tex] and [tex]\((8,2)\)[/tex]:
[tex]\[ \text{slope} = \frac{2 - 0}{8 - 3} = \frac{2}{5} = 0.4 \][/tex]
The slope is [tex]\(0.4\)[/tex]. This is equal to [tex]\(0.4\)[/tex], therefore, they are parallel.
3. Conclusion:
The ordered pairs that could be points on a line parallel to the line containing [tex]\((3,4)\)[/tex] and [tex]\((-2,2)\)[/tex] are:
- [tex]\((-1,1)\)[/tex] and [tex]\((-6,-1)\)[/tex]
- [tex]\((1,0)\)[/tex] and [tex]\((6,2)\)[/tex]
- [tex]\((3,0)\)[/tex] and [tex]\((8,2)\)[/tex]
These are the pairs with slopes equal to [tex]\(0.4\)[/tex].
1. Calculate the slope of the line through [tex]\((3,4)\)[/tex] and [tex]\((-2,2)\)[/tex]
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 4}{-2 - 3} = \frac{-2}{-5} = 0.4 \][/tex]
Next, we will calculate the slopes of the lines formed by each pair of points and compare them to the calculated slope [tex]\(0.4\)[/tex]. If the slopes are equal, the lines are parallel.
2. Calculate the slopes for given pairs and compare:
- For [tex]\((-2,-5)\)[/tex] and [tex]\((-7,-3)\)[/tex]:
[tex]\[ \text{slope} = \frac{-3 - (-5)}{-7 - (-2)} = \frac{-3 + 5}{-7 + 2} = \frac{2}{-5} = -0.4 \][/tex]
The slope is [tex]\(-0.4\)[/tex]. This is not equal to [tex]\(0.4\)[/tex], therefore, they are not parallel.
- For [tex]\((-1,1)\)[/tex] and [tex]\((-6,-1)\)[/tex]:
[tex]\[ \text{slope} = \frac{-1 - 1}{-6 - (-1)} = \frac{-1 - 1}{-6 + 1} = \frac{-2}{-5} = 0.4 \][/tex]
The slope is [tex]\(0.4\)[/tex]. This is equal to [tex]\(0.4\)[/tex], therefore, they are parallel.
- For [tex]\((0,0)\)[/tex] and [tex]\((2,5)\)[/tex]:
[tex]\[ \text{slope} = \frac{5 - 0}{2 - 0} = \frac{5}{2} = 2.5 \][/tex]
The slope is [tex]\(2.5\)[/tex]. This is not equal to [tex]\(0.4\)[/tex], therefore, they are not parallel.
- For [tex]\((1,0)\)[/tex] and [tex]\((6,2)\)[/tex]:
[tex]\[ \text{slope} = \frac{2 - 0}{6 - 1} = \frac{2}{5} = 0.4 \][/tex]
The slope is [tex]\(0.4\)[/tex]. This is equal to [tex]\(0.4\)[/tex], therefore, they are parallel.
- For [tex]\((3,0)\)[/tex] and [tex]\((8,2)\)[/tex]:
[tex]\[ \text{slope} = \frac{2 - 0}{8 - 3} = \frac{2}{5} = 0.4 \][/tex]
The slope is [tex]\(0.4\)[/tex]. This is equal to [tex]\(0.4\)[/tex], therefore, they are parallel.
3. Conclusion:
The ordered pairs that could be points on a line parallel to the line containing [tex]\((3,4)\)[/tex] and [tex]\((-2,2)\)[/tex] are:
- [tex]\((-1,1)\)[/tex] and [tex]\((-6,-1)\)[/tex]
- [tex]\((1,0)\)[/tex] and [tex]\((6,2)\)[/tex]
- [tex]\((3,0)\)[/tex] and [tex]\((8,2)\)[/tex]
These are the pairs with slopes equal to [tex]\(0.4\)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
