To find the distance between the points [tex]\((6, -2)\)[/tex] and [tex]\((1, -2)\)[/tex], we can use the distance formula. The distance formula is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here are the coordinates of the points:
- [tex]\((x_1, y_1) = (6, -2)\)[/tex]
- [tex]\((x_2, y_2) = (1, -2)\)[/tex]
Let's plug these values into the distance formula:
1. Subtract the [tex]\(x\)[/tex]-coordinates:
[tex]\[ x_2 - x_1 = 1 - 6 = -5 \][/tex]
2. Subtract the [tex]\(y\)[/tex]-coordinates:
[tex]\[ y_2 - y_1 = -2 - (-2) = 0 \][/tex]
3. Square the differences:
[tex]\[ (x_2 - x_1)^2 = (-5)^2 = 25 \][/tex]
[tex]\[ (y_2 - y_1)^2 = 0^2 = 0 \][/tex]
4. Add the squared differences:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 25 + 0 = 25 \][/tex]
5. Finally, take the square root of the sum:
[tex]\[ d = \sqrt{25} = 5 \][/tex]
Therefore, the distance between the points [tex]\((6, -2)\)[/tex] and [tex]\((1, -2)\)[/tex] is [tex]\(5\)[/tex] units.
The correct answer is:
[tex]\[ \boxed{5 \text{ units}} \][/tex]
