Question

calculate the distance between the points j = (-1, 4) and e = (2, -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 \( J = (-1, 4) \), \( x_1 = -1 \), \( y_1 = 4 \); for \( E = (2, -1) \), \( x_2 = 2 \), \( y_2 = -1 \).

Step3: Substitute into formula

\( d = \sqrt{(2 - (-1))^2 + (-1 - 4)^2} = \sqrt{(3)^2 + (-5)^2} \)

Step4: Simplify

\( \sqrt{9 + 25} = \sqrt{34} \)

Answer:

\(\sqrt{34}\)