Question

find the distance, d, of \\( \overline { a b } \\).
\\( a = ( - 3,4 ) \quad b = ( 5,8 ) \\)
\\( d = \\) ?
\\( d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } \\)
round to the nearest tenth.

Explanation:

Step1: Identify the coordinates

\(x_1=-3,y_1 = 4,x_2=5,y_2 = 8\)

Step2: Substitute into the distance formula

$$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(5-(-3))^2+(8 - 4)^2}$$

Step3: Simplify the expression inside the square - root

First, calculate \((5-(-3))=5 + 3=8\) and \((8 - 4)=4\). Then \((x_2 - x_1)^2+(y_2 - y_1)^2=8^2+4^2=64 + 16=80\)

Step4: Calculate the square - root

\(d=\sqrt{80}\approx8.944\)

Step5: Round to the nearest tenth

Rounding \(8.944\) to the nearest tenth gives \(d\approx8.9\)

Answer:

\(8.9\)