Question

find the distance between the pair of points.
a(0,2), b(0,8)
d = \square (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

The coordinates of point \( A \) are \( (0, 2) \) and point \( B \) are \( (0, 8) \). So, \( x_1 = 0 \), \( y_1 = 2 \), \( x_2 = 0 \), \( y_2 = 8 \).

Step2: Use the distance formula

The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Substitute the values: \( d=\sqrt{(0 - 0)^2+(8 - 2)^2} \)

Step3: Simplify the expression

First, calculate the differences: \( 0 - 0 = 0 \) and \( 8 - 2 = 6 \).
Then, square the differences: \( 0^2 = 0 \) and \( 6^2 = 36 \).
Add the results: \( 0 + 36 = 36 \).
Take the square root: \( d=\sqrt{36}=6 \)

Answer:

\( 6 \)