To determine the distance between the two points [tex]\((1, 8)\)[/tex] and [tex]\((7, 8)\)[/tex], we can use the distance formula which is derived from the Pythagorean theorem.
The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a Cartesian coordinate plane is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given the coordinates of the points:
- Point 1: [tex]\((x_1, y_1) = (1, 8)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (7, 8)\)[/tex]
We substitute these values into the distance formula:
[tex]\[ \text{Distance} = \sqrt{(7 - 1)^2 + (8 - 8)^2} \][/tex]
First, compute the differences inside the parentheses:
[tex]\[ 7 - 1 = 6 \][/tex]
[tex]\[ 8 - 8 = 0 \][/tex]
Now, square these differences:
[tex]\[ (7 - 1)^2 = 6^2 = 36 \][/tex]
[tex]\[ (8 - 8)^2 = 0^2 = 0 \][/tex]
Add the squared terms together:
[tex]\[ 36 + 0 = 36 \][/tex]
Finally, take the square root of the sum:
[tex]\[ \sqrt{36} = 6 \][/tex]
Thus, the distance between the points [tex]\((1, 8)\)[/tex] and [tex]\((7, 8)\)[/tex] is [tex]\(6.0\)[/tex].
