Question

calculate the distance between the points n = (3, -2) and h = (7, -9) 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 \( N=(3, -2) \), \( x_1 = 3 \), \( y_1 = -2 \); for \( H=(7, -9) \), \( x_2 = 7 \), \( y_2 = -9 \).

Step3: Substitute into formula

\( d = \sqrt{(7 - 3)^2 + (-9 - (-2))^2} = \sqrt{4^2 + (-7)^2} \)

Step4: Simplify

\( \sqrt{16 + 49} = \sqrt{65} \)

Answer:

\(\sqrt{65}\)