Let's find the distance between the two points [tex]\((-10, -7)\)[/tex] and [tex]\((-8, 1)\)[/tex].
1. Identify the coordinates of the two points:
- First point [tex]\((x_1, y_1)\)[/tex] is [tex]\((-10, -7)\)[/tex]
- Second point [tex]\((x_2, y_2)\)[/tex] is [tex]\((-8, 1)\)[/tex]
2. Calculate the differences in the x-coordinates ([tex]\(\Delta x\)[/tex]) and y-coordinates ([tex]\(\Delta y\)[/tex]):
- [tex]\(\Delta x = x_2 - x_1 = -8 - (-10) = -8 + 10 = 2\)[/tex]
- [tex]\(\Delta y = y_2 - y_1 = 1 - (-7) = 1 + 7 = 8\)[/tex]
3. Apply the distance formula, which is:
[tex]\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\][/tex]
Here, [tex]\(\Delta x = 2\)[/tex] and [tex]\(\Delta y = 8\)[/tex]:
[tex]\[
d = \sqrt{(2)^2 + (8)^2} = \sqrt{4 + 64} = \sqrt{68}
\][/tex]
4. Evaluate the square root to find the exact distance:
[tex]\[
\sqrt{68} \approx 8.246211251235321
\][/tex]
5. Round the result to the nearest tenth:
[tex]\[
8.2
\][/tex]
Thus, the distance between the points [tex]\((-10, -7)\)[/tex] and [tex]\((-8, 1)\)[/tex] is approximately [tex]\(8.2\)[/tex] units.
