Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To find the distance between two points \( A(5,8) \) and \( B(-3,4) \) in a Cartesian plane, you can use the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, \((x_1, y_1)\) are the coordinates of point \( A \) and \((x_2, y_2)\) are the coordinates of point \( B \).
1. Identify the coordinates of the points:
- Point \( A \) has coordinates \((5, 8)\).
- Point \( B \) has coordinates \((-3, 4)\).
2. Substitute these coordinates into the distance formula:
[tex]\[ d = \sqrt{(-3 - 5)^2 + (4 - 8)^2} \][/tex]
3. Calculate the differences inside the parentheses:
[tex]\[ x_2 - x_1 = -3 - 5 = -8 \][/tex]
[tex]\[ y_2 - y_1 = 4 - 8 = -4 \][/tex]
4. Substitute these differences back into the formula:
[tex]\[ d = \sqrt{(-8)^2 + (-4)^2} \][/tex]
5. Square these differences:
[tex]\[ (-8)^2 = 64 \][/tex]
[tex]\[ (-4)^2 = 16 \][/tex]
6. Add the squared differences:
[tex]\[ 64 + 16 = 80 \][/tex]
7. Finally, take the square root of the sum to find the distance:
[tex]\[ d = \sqrt{80} \][/tex]
8. Simplifying the square root of 80:
[tex]\[ d = \sqrt{16 \times 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \][/tex]
9. Approximating further to a numerical value, we get:
[tex]\[ d \approx 8.94427190999916 \][/tex]
Therefore, the distance between the points [tex]\( A(5,8) \)[/tex] and [tex]\( B(-3,4) \)[/tex] is approximately [tex]\( 8.94427190999916 \)[/tex] units.
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, \((x_1, y_1)\) are the coordinates of point \( A \) and \((x_2, y_2)\) are the coordinates of point \( B \).
1. Identify the coordinates of the points:
- Point \( A \) has coordinates \((5, 8)\).
- Point \( B \) has coordinates \((-3, 4)\).
2. Substitute these coordinates into the distance formula:
[tex]\[ d = \sqrt{(-3 - 5)^2 + (4 - 8)^2} \][/tex]
3. Calculate the differences inside the parentheses:
[tex]\[ x_2 - x_1 = -3 - 5 = -8 \][/tex]
[tex]\[ y_2 - y_1 = 4 - 8 = -4 \][/tex]
4. Substitute these differences back into the formula:
[tex]\[ d = \sqrt{(-8)^2 + (-4)^2} \][/tex]
5. Square these differences:
[tex]\[ (-8)^2 = 64 \][/tex]
[tex]\[ (-4)^2 = 16 \][/tex]
6. Add the squared differences:
[tex]\[ 64 + 16 = 80 \][/tex]
7. Finally, take the square root of the sum to find the distance:
[tex]\[ d = \sqrt{80} \][/tex]
8. Simplifying the square root of 80:
[tex]\[ d = \sqrt{16 \times 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \][/tex]
9. Approximating further to a numerical value, we get:
[tex]\[ d \approx 8.94427190999916 \][/tex]
Therefore, the distance between the points [tex]\( A(5,8) \)[/tex] and [tex]\( B(-3,4) \)[/tex] is approximately [tex]\( 8.94427190999916 \)[/tex] units.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.