To determine the distance between the two points [tex]\((-6, 8)\)[/tex] and [tex]\((-6, -3)\)[/tex], we follow these steps:
1. Identify the coordinates of the points:
- Point [tex]\(A\)[/tex] has coordinates [tex]\((-6, 8)\)[/tex]
- Point [tex]\(B\)[/tex] has coordinates [tex]\((-6, -3)\)[/tex]
2. Understand the relationship between these points:
Since both points share the same [tex]\(x\)[/tex]-coordinate ([tex]\(-6\)[/tex]), they lie on a vertical line. This simplifies the calculation, as we only need to consider the difference in the [tex]\(y\)[/tex]-coordinates.
3. Calculate the difference in [tex]\(y\)[/tex]-coordinates:
- The [tex]\(y\)[/tex]-coordinate of point [tex]\(A\)[/tex] is [tex]\(8\)[/tex]
- The [tex]\(y\)[/tex]-coordinate of point [tex]\(B\)[/tex] is [tex]\(-3\)[/tex]
The distance between the points can be calculated by finding the absolute difference between the [tex]\(y\)[/tex]-coordinates:
[tex]\[
\text{Distance} = \left|8 - (-3)\right|
\][/tex]
4. Perform the subtraction and calculate the absolute value:
[tex]\[
\left|8 - (-3)\right| = \left|8 + 3\right| = \left|11\right| = 11
\][/tex]
Therefore, the distance between the points [tex]\((-6, 8)\)[/tex] and [tex]\((-6, -3)\)[/tex] is [tex]\(11\)[/tex] units.
