To find the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] on a coordinate plane, we use the distance formula:
[tex]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Given the points [tex]\((2, 1)\)[/tex] and [tex]\((14, 6)\)[/tex], let's identify the coordinates:
- [tex]\((x_1, y_1) = (2, 1)\)[/tex]
- [tex]\((x_2, y_2) = (14, 6)\)[/tex]
Now, apply the coordinates to the distance formula:
1. Compute the difference in the x-coordinates:
[tex]\[
x_2 - x_1 = 14 - 2 = 12
\][/tex]
2. Compute the difference in the y-coordinates:
[tex]\[
y_2 - y_1 = 6 - 1 = 5
\][/tex]
3. Square these differences:
[tex]\[
(12)^2 = 144
\][/tex]
[tex]\[
(5)^2 = 25
\][/tex]
4. Add the squared differences:
[tex]\[
144 + 25 = 169
\][/tex]
5. Take the square root of the sum:
[tex]\[
\sqrt{169} = 13
\][/tex]
Therefore, the distance between the points [tex]\((2, 1)\)[/tex] and [tex]\((14, 6)\)[/tex] is [tex]\(\boxed{13}\)[/tex] units.
So, the correct answer is:
A. 13 units
