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 } ) ^ { 2 } } \\)
round to the nearest tenth.

Explanation:

Step1: Identify the coordinates

$A=(x_1,y_1)=(5,4)$ and $B=(x_2,y_2)=(14,0)$

Step2: Substitute into the distance formula

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

Step3: Calculate the values inside the square - root

$(14 - 5)=9$ and $(0 - 4)=-4$. Then $(14 - 5)^2+(0 - 4)^2=9^2+(-4)^2=81 + 16=97$

Step4: Calculate the square - root

$d=\sqrt{97}\approx9.8$ (rounded to the nearest tenth)

Answer:

$9.8$