To find the distance between the points [tex]\((3, 4)\)[/tex] and [tex]\((-8, 4)\)[/tex], follow these steps using the distance formula:
The distance formula between two points [tex]\((x1, y1)\)[/tex] and [tex]\((x2, y2)\)[/tex] is given by:
[tex]\[ \text{Distance} = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \][/tex]
Here are the coordinates:
- The first point [tex]\((x1, y1)\)[/tex] is [tex]\((3, 4)\)[/tex]
- The second point [tex]\((x2, y2)\)[/tex] is [tex]\((-8, 4)\)[/tex]
Step-by-Step Solution:
1. Identify the coordinates:
- [tex]\(x1 = 3\)[/tex], [tex]\(y1 = 4\)[/tex]
- [tex]\(x2 = -8\)[/tex], [tex]\(y2 = 4\)[/tex]
2. Substitute the coordinates into the distance formula:
[tex]\[ \text{Distance} = \sqrt{(-8 - 3)^2 + (4 - 4)^2} \][/tex]
3. Calculate the differences:
- For [tex]\(x\)[/tex] coordinates: [tex]\((-8 - 3) = -11\)[/tex]
- For [tex]\(y\)[/tex] coordinates: [tex]\((4 - 4) = 0\)[/tex]
4. Square the differences:
- [tex]\((-11)^2 = 121\)[/tex]
- [tex]\(0^2 = 0\)[/tex]
5. Add the squared differences:
[tex]\[ 121 + 0 = 121 \][/tex]
6. Take the square root of the sum:
[tex]\[ \sqrt{121} = 11 \][/tex]
Thus, the distance between the points [tex]\((3, 4)\)[/tex] and [tex]\((-8, 4)\)[/tex] is:
[tex]\[ 11 \][/tex]
