Question

find the distance, d, of \\( \overline { a b } \\).
\\( a = ( 1,1 ) \\) \\( b = ( 7,13 ) \\)
\\( d = \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } \\)
round to the nearest tenth.

Explanation:

Step1: Identify the coordinates

$x_1 = 1,y_1 = 1,x_2 = 7,y_2 = 13$

Step2: Substitute into the distance formula

$$d=\sqrt{(7 - 1)^2+(13 - 1)^2}$$

Step3: Calculate the squares

$(7 - 1)^2=36$，$(13 - 1)^2 = 144$

Step4: Add the results

$36+144 = 180$

Step5: Take the square root

$d=\sqrt{180}\approx13.4$

Answer:

$13.4$