To find the distance between the points [tex]\((3, 4)\)[/tex] and [tex]\((-8, 4)\)[/tex], you can use the distance formula. The distance formula is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point, and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point.
Let's break it down step by step:
1. Identify the coordinates:
- Point 1: [tex]\((x_1, y_1) = (3, 4)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-8, 4)\)[/tex]
2. Subtract the coordinates:
- For [tex]\(x\)[/tex]-coordinates: [tex]\( x_2 - x_1 = -8 - 3 \)[/tex]
- For [tex]\(y\)[/tex]-coordinates: [tex]\( y_2 - y_1 = 4 - 4 \)[/tex]
3. Calculate the differences:
- [tex]\( x_2 - x_1 = -8 - 3 = -11 \)[/tex]
- [tex]\( y_2 - y_1 = 4 - 4 = 0 \)[/tex]
4. Square the differences:
- [tex]\((x_2 - x_1)^2 = (-11)^2 = 121\)[/tex]
- [tex]\((y_2 - y_1)^2 = (0)^2 = 0\)[/tex]
5. Add the squared differences:
- [tex]\((x_2 - x_1)^2 + (y_2 - y_1)^2 = 121 + 0 = 121\)[/tex]
6. Take the square root of the sum:
- [tex]\(\sqrt{121} = 11\)[/tex]
Therefore, the distance between the points [tex]\((3, 4)\)[/tex] and [tex]\((-8, 4)\)[/tex] is [tex]\(\boxed{11}\)[/tex].
