Question

find the distance, d, of \\(\overline{ab}\\). \\(a = (1, 0)\\) \\(b = (5, 2)\\) \\(d = ?\\) \\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\) round to the nearest tenth

Explanation:

Step1: Identify coordinates

Let \( A=(x_1,y_1)=(1,0) \), \( B=(x_2,y_2)=(5,2) \).

Step2: Apply distance formula

Substitute into \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \):
\( d = \sqrt{(5 - 1)^2 + (2 - 0)^2} \)

Step3: Simplify inside the square root

Calculate \( (5 - 1)^2 = 16 \), \( (2 - 0)^2 = 4 \).
So \( d = \sqrt{16 + 4} = \sqrt{20} \)

Step4: Approximate to nearest tenth

\( \sqrt{20} \approx 4.5 \) (since \( 4.47^2 \approx 20 \), rounded to tenth is 4.5).

Answer:

\( 4.5 \)