Question

find the distance, d, of \\( \overline { a b } \\).
\\( a = ( - 2, - 10 ) \\) \\( b = ( - 6,0 ) \\)
\\( d = \\)
\\( d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } \\)
round to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Given \(A=(-2,-10)\) and \(B = (-6,0)\). Let \((x_1,y_1)=(-2,-10)\) and \((x_2,y_2)=(-6,0)\).

Step2: Substitute into the distance formula

The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(x_2 - x_1=-6-(-2)=-6 + 2=-4\), \(y_2 - y_1=0-(-10)=10\).
So \(d=\sqrt{(-4)^2+10^2}\).

Step3: Calculate the squares

\((-4)^2 = 16\) and \(10^2=100\). Then \(d=\sqrt{16 + 100}\).

Step4: Sum and take the square - root

\(16+100 = 116\), so \(d=\sqrt{116}\approx10.8\) (rounded to the nearest tenth).

Answer:

$10.8$