Question

find the distance, d, of \\( \overline { a b } \\).
\\( a = ( 2,1 ) \\) \\( b = ( - 4,7 ) \\)
\\( d = \\)
\\( d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } \\)
round to the nearest tenth

Explanation:

Step1: Identify coordinates

Let \(A=(x_1,y_1)=(2,1)\) and \(B=(x_2,y_2)=(-4,7)\).

Step2: Substitute into distance formula

Substitute \(x_1 = 2\), \(y_1 = 1\), \(x_2=-4\), \(y_2 = 7\) into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

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Step3: Simplify and round

\(\sqrt{72}\approx8.5\) (rounded to the nearest tenth).

Answer:

\(8.5\)