Question

calculate the distance between the points j=(0, 6) and n=(-7, 1) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify coordinates

For \( J=(0, 6) \), \( x_1 = 0 \), \( y_1 = 6 \); for \( N=(-7, 1) \), \( x_2 = -7 \), \( y_2 = 1 \).

Step3: Substitute into formula

\( d = \sqrt{(-7 - 0)^2 + (1 - 6)^2} = \sqrt{(-7)^2 + (-5)^2} \)

Step4: Simplify squares

\( \sqrt{49 + 25} = \sqrt{74} \)

Answer:

\(\sqrt{74}\)