To find the distance between points A(2, 3) and B(5, 9), follow these steps:
1. Identify the coordinates of the points:
- Point A has coordinates (2, 3)
- Point B has coordinates (5, 9)
2. Calculate the differences in the x-coordinates and y-coordinates:
- Difference in x-coordinates (Δx): [tex]\( x_2 - x_1 = 5 - 2 = 3 \)[/tex]
- Difference in y-coordinates (Δy): [tex]\( y_2 - y_1 = 9 - 3 = 6 \)[/tex]
3. Use the distance formula to find the distance between the points:
[tex]\[
\text{Distance} = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\][/tex]
Substituting the differences, we get:
[tex]\[
\text{Distance} = \sqrt{(3)^2 + (6)^2} = \sqrt{9 + 36} = \sqrt{45}
\][/tex]
4. Simplify the square root:
[tex]\[
\sqrt{45} \approx 6.708203932499369
\][/tex]
5. Round the result to the nearest tenth:
[tex]\[
6.708203932499369 \approx 6.7
\][/tex]
Therefore, the distance between points A and B, rounded to the nearest tenth, is [tex]\( 6.7 \)[/tex] units.
