Question

for each of the following pairs of points, find the length of \\( \overline { a b } \\).
a. \\( a ( 0,3 ) , b ( 0,2 ) \\)
b. \\( a ( 0,9 ) , b ( 12,0 ) \\)
c. \\( a ( - 21,12 ) , b ( - 25,11 ) \\)
a. the length of \\( \overline { a b } \\) is \\( \square \\)
(type an exact answer, using radicals as needed. simplify your answer)

Explanation:

Step1: Recall the distance formula

The distance formula between two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(A(0,3)\) and \(B(0,2)\), here \(x_1 = 0,y_1=3,x_2 = 0,y_2 = 2\).

Step2: Substitute the values into the formula

Substitute into the formula: \(d=\sqrt{(0 - 0)^2+(2 - 3)^2}\).
First, calculate \((0 - 0)^2=0\) and \((2 - 3)^2=(-1)^2 = 1\).
Then \(d=\sqrt{0 + 1}\).

Answer:

\(1\)