To find the distance [tex]\(d\)[/tex] between points [tex]\(A (-2, -10)\)[/tex] and [tex]\(B (-6, 0)\)[/tex], we will utilize the distance formula:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Given the coordinates of the points, we have:
- [tex]\(x_1 = -2\)[/tex]
- [tex]\(y_1 = -10\)[/tex]
- [tex]\(x_2 = -6\)[/tex]
- [tex]\(y_2 = 0\)[/tex]
Step-by-step, let's calculate the distance:
1. Calculate the difference in the x-coordinates (horizontal distance):
[tex]\[
x_2 - x_1 = -6 - (-2) = -6 + 2 = -4
\][/tex]
So, the horizontal distance is [tex]\(-4\)[/tex].
2. Calculate the difference in the y-coordinates (vertical distance):
[tex]\[
y_2 - y_1 = 0 - (-10) = 0 + 10 = 10
\][/tex]
So, the vertical distance is [tex]\(10\)[/tex].
3. Square these distances:
[tex]\[
(-4)^2 = 16
\][/tex]
[tex]\[
10^2 = 100
\][/tex]
4. Sum these squared distances:
[tex]\[
16 + 100 = 116
\][/tex]
5. Take the square root of the sum to find the distance:
[tex]\[
d = \sqrt{116} \approx 10.770329614269007
\][/tex]
6. Round the result to the nearest tenth:
[tex]\[
d \approx 10.8
\][/tex]
Therefore, the distance [tex]\(d\)[/tex] between points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is:
[tex]\[
\boxed{10.8}
\][/tex]
