To find the distance between the two points [tex]\((7, -7)\)[/tex] and [tex]\((1, 2)\)[/tex], we will use the Euclidean distance formula. Here is a detailed step-by-step solution:
1. Identify the coordinates:
- Point 1: [tex]\((x_1, y_1) = (7, -7)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (1, 2)\)[/tex]
2. Calculate the differences in the coordinates:
- Difference in x-coordinates: [tex]\( dx = x_2 - x_1 = 1 - 7 = -6 \)[/tex]
- Difference in y-coordinates: [tex]\( dy = y_2 - y_1 = 2 - (-7) = 2 + 7 = 9 \)[/tex]
3. Apply the Euclidean distance formula:
- The distance [tex]\( d \)[/tex] between the two points is given by:
[tex]\[
d = \sqrt{(dx)^2 + (dy)^2} = \sqrt{(-6)^2 + 9^2} = \sqrt{36 + 81} = \sqrt{117}
\][/tex]
4. Calculate the exact distance:
- Simplify the expression under the square root:
[tex]\[
\sqrt{117} \approx 10.816653826391969
\][/tex]
5. Round the distance to the nearest tenth:
- The decimal value [tex]\( 10.816653826391969 \)[/tex] rounded to the nearest tenth is [tex]\( 10.8 \)[/tex].
Therefore, the distance between the points [tex]\((7, -7)\)[/tex] and [tex]\((1, 2)\)[/tex], rounded to the nearest tenth, is [tex]\( 10.8 \)[/tex].
Answer:
[tex]\[
\boxed{10.8}
\][/tex]
