Question

find the distance, d, of \\(\overline{ab}\\).\
a = (3, 11) b = (1, 5)\
d = ?\
\\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\)\
round to the nearest tenth.

Explanation:

Step1: Identify coordinates

Let \( A=(x_1,y_1)=(3,11) \), \( B=(x_2,y_2)=(1,5) \).

Step2: Apply distance formula

Use \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Substitute values: \( d = \sqrt{(1 - 3)^2 + (5 - 11)^2} \).

Step3: Simplify inside the square root

Calculate \( (1 - 3)^2 = (-2)^2 = 4 \), \( (5 - 11)^2 = (-6)^2 = 36 \).
Sum: \( 4 + 36 = 40 \).

Step4: Take square root and round

\( d = \sqrt{40} \approx 6.3 \) (rounded to nearest tenth).

Answer:

\( 6.3 \)