To find the distance between the two points [tex]\((-3, 3)\)[/tex] and [tex]\( (6, 7) \)[/tex], we can use the distance formula. The distance formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's follow the steps:
1. Identify the coordinates of the points:
- Point 1: [tex]\((x_1, y_1) = (-3, 3)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (6, 7)\)[/tex]
2. Calculate the differences in the coordinates:
- Difference in [tex]\(x\)[/tex]: [tex]\( x_2 - x_1 = 6 - (-3) = 6 + 3 = 9 \)[/tex]
- Difference in [tex]\(y\)[/tex]: [tex]\( y_2 - y_1 = 7 - 3 = 4 \)[/tex]
3. Substitute the values into the distance formula:
[tex]\[ d = \sqrt{(9)^2 + (4)^2} \][/tex]
4. Compute the squares and the sum inside the square root:
[tex]\[ d = \sqrt{81 + 16} \][/tex]
[tex]\[ d = \sqrt{97} \][/tex]
5. Calculate the square root:
[tex]\[ d \approx 9.848857801796104 \][/tex]
6. Round the result to the nearest tenth:
[tex]\[ d \approx 9.8 \][/tex]
Thus, the distance between the points [tex]\((-3, 3)\)[/tex] and [tex]\((6, 7)\)[/tex], rounded to the nearest tenth, is [tex]\(9.8\)[/tex].
