Question

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

Explanation:

Step1: Substitute the coordinates into the distance formula

Given \(A=(-5,5)\) and \(B=(5,-5)\), substitute \(x_1=-5,y_1 = 5,x_2=5,y_2=-5\) into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

$$d=\sqrt{(5-(-5))^2+(-5 - 5)^2}$$

Step2: Simplify the expressions inside the square - root

First, simplify \(5-(-5)=5 + 5=10\) and \(-5-5=-10\). Then the formula becomes \(d=\sqrt{10^2+(-10)^2}\).
Since \(10^2 = 100\) and \((-10)^2=100\), we have \(d=\sqrt{100 + 100}\).

Step3: Calculate the value of \(d\)

\(d=\sqrt{200}\approx14.1421\). Rounding \(14.1421\) to the nearest tenth gives \(d\approx14.1\).

Answer:

$14.1$