Question

find the distance, d, of \\( \overline { a b } \\).
\\( a = ( - 5,1 ) \\) \\( b = ( 1, - 3 ) \\)
\\( d = \\)
\\( d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } \\)
round to the nearest tenth

Explanation:

Step1: Identify coordinates

Let \(A=(x_1,y_1)=(-5,1)\) and \(B=(x_2,y_2)=(1,-3)\)

Step2: Substitute into distance formula

\(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(1-(-5))^2+(-3 - 1)^2}\)
\(=\sqrt{(1 + 5)^2+(-4)^2}=\sqrt{6^2+(-4)^2}\)
\(=\sqrt{36 + 16}=\sqrt{52}\)

Step3: Simplify and round

\(\sqrt{52}\approx7.2\)

Answer:

\(7.2\)