Sure, let's find the distance between points [tex]\(A(2, 3)\)[/tex] and [tex]\(B(5, 9)\)[/tex]. We'll use the distance formula:
The distance formula between 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 break down each step:
1. Identify the coordinates of the points:
- Point A: [tex]\( (x_1, y_1) = (2, 3) \)[/tex]
- Point B: [tex]\( (x_2, y_2) = (5, 9) \)[/tex]
2. Calculate the difference in the x-coordinates:
[tex]\[ x_2 - x_1 = 5 - 2 = 3 \][/tex]
3. Calculate the difference in the y-coordinates:
[tex]\[ y_2 - y_1 = 9 - 3 = 6 \][/tex]
4. Square each difference:
[tex]\[ (x_2 - x_1)^2 = 3^2 = 9 \][/tex]
[tex]\[ (y_2 - y_1)^2 = 6^2 = 36 \][/tex]
5. Sum the squares of the differences:
[tex]\[ 9 + 36 = 45 \][/tex]
6. Take the square root of the sum to find the distance:
[tex]\[ d = \sqrt{45} \approx 6.708203932499369 \][/tex]
7. Round the result to the nearest tenth:
[tex]\[ d \approx 6.7 \][/tex]
Therefore, the distance between points [tex]\(A(2, 3)\)[/tex] and [tex]\(B(5, 9)\)[/tex], rounded to the nearest tenth, is [tex]\(6.7\)[/tex].
