To find the distance between the points [tex]\( A(1, 5) \)[/tex] and [tex]\( B(5.5, 9.25) \)[/tex], you 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 go through the calculation step-by-step:
1. Identify the coordinates of the points:
- Point [tex]\( A \)[/tex] has coordinates [tex]\((x_1, y_1) = (1, 5)\)[/tex]
- Point [tex]\( B \)[/tex] has coordinates [tex]\((x_2, y_2) = (5.5, 9.25)\)[/tex]
2. Calculate the difference in the [tex]\( x \)[/tex]-coordinates and the [tex]\( y \)[/tex]-coordinates:
[tex]\[
\Delta x = x_2 - x_1 = 5.5 - 1 = 4.5
\][/tex]
[tex]\[
\Delta y = y_2 - y_1 = 9.25 - 5 = 4.25
\][/tex]
3. Square the differences:
[tex]\[
(\Delta x)^2 = (4.5)^2 = 20.25
\][/tex]
[tex]\[
(\Delta y)^2 = (4.25)^2 = 18.0625
\][/tex]
4. Add the squared differences:
[tex]\[
20.25 + 18.0625 = 38.3125
\][/tex]
5. Take the square root of the sum to find the distance:
[tex]\[
d = \sqrt{38.3125} \approx 6.1904
\][/tex]
6. Round the distance to the nearest tenth:
[tex]\[
d \approx 6.2
\][/tex]
Therefore, the distance between the points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is approximately [tex]\( 6.2 \)[/tex] units when rounded to the nearest tenth.
