To find the distance between the two points [tex]\((5, -8)\)[/tex] and [tex]\((-3, -1)\)[/tex], we will use the distance formula, which is:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given points:
- [tex]\((x_1, y_1) = (5, -8)\)[/tex]
- [tex]\((x_2, y_2) = (-3, -1)\)[/tex]
Step-by-step solution:
1. Calculate the differences between the x-coordinates and y-coordinates:
[tex]\[
x_2 - x_1 = -3 - 5 = -8
\][/tex]
[tex]\[
y_2 - y_1 = -1 - (-8) = -1 + 8 = 7
\][/tex]
2. Square these differences:
[tex]\[
(x_2 - x_1)^2 = (-8)^2 = 64
\][/tex]
[tex]\[
(y_2 - y_1)^2 = 7^2 = 49
\][/tex]
3. Sum the squared differences:
[tex]\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 64 + 49 = 113
\][/tex]
4. Take the square root of the sum to find the distance:
[tex]\[
d = \sqrt{113} \approx 10.63014581273465
\][/tex]
5. Round the distance to the nearest tenth:
[tex]\[
d \approx 10.6
\][/tex]
Therefore, the distance between the points [tex]\((5, -8)\)[/tex] and [tex]\((-3, -1)\)[/tex], rounded to the nearest tenth, is [tex]\(10.6\)[/tex].
