Question

find the distance, d, of \\( \overline { a b } \\).
\\( a = ( 5,4 ) \quad b = ( 14,0 ) \\)
\\( d = \\)
\\( d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) } \\)

Explanation:

Step1: Identify coordinates

$x_1 = 5$, $y_1 = 4$, $x_2 = 14$, $y_2 = 0$

Step2: Substitute into distance formula

$$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(14 - 5)^2+(0 - 4)^2}$$

Step3: Calculate values inside the square root

$(14 - 5)^2=81$, $(0 - 4)^2 = 16$
$$d=\sqrt{81 + 16}=\sqrt{97}$$

Step4: Approximate the value

$\sqrt{97}\approx9.8$

Answer:

$9.8$