To find the distance between the two points [tex]\((1, 2)\)[/tex] and [tex]\((-5, -2)\)[/tex], we can use the distance formula. The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let's apply this step-by-step:
1. Identify the coordinates:
- Point 1: [tex]\((x_1, y_1) = (1, 2)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-5, -2)\)[/tex]
2. Calculate the differences in the x-coordinates and y-coordinates:
- [tex]\( \Delta x = x_2 - x_1 = -5 - 1 = -6 \)[/tex]
- [tex]\( \Delta y = y_2 - y_1 = -2 - 2 = -4 \)[/tex]
3. Substitute these differences into the distance formula:
[tex]\[
d = \sqrt{(-6)^2 + (-4)^2}
\][/tex]
4. Simplify inside the square root:
[tex]\[
d = \sqrt{36 + 16}
\][/tex]
[tex]\[
d = \sqrt{52}
\][/tex]
5. Calculate the square root:
[tex]\[
d = \sqrt{52} \approx 7.211102550927978
\][/tex]
6. Round the distance to the nearest tenth (if necessary):
[tex]\[
d \approx 7.2
\][/tex]
Thus, the distance between the points [tex]\((1, 2)\)[/tex] and [tex]\((-5, -2)\)[/tex], rounded to the nearest tenth, is [tex]\(7.2\)[/tex].
