Question

find the distance, d, of \\(\overline{ab}\\).\\(a = (-7, 9)\\) \\(b = (-5, 3)\\)\\(d = ?\\)\\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\)round to the nearest tenth

Explanation:

Step1: Identify coordinates

Let \( A = (x_1, y_1) = (-7, 9) \) and \( B = (x_2, y_2) = (-5, 3) \).

Step2: Apply distance formula

Use \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Substitute values: \( x_2 - x_1 = -5 - (-7) = 2 \), \( y_2 - y_1 = 3 - 9 = -6 \).

Step3: Calculate squares

\( (x_2 - x_1)^2 = 2^2 = 4 \), \( (y_2 - y_1)^2 = (-6)^2 = 36 \).

Step4: Sum and square root

Sum: \( 4 + 36 = 40 \). Then \( d = \sqrt{40} \approx 6.3 \) (rounded to nearest tenth).

Answer:

\( 6.3 \)