Question

reminder: be sure to simplify the radical to get your final answer. what is the distance between points e and l? options: 16√4, 2√4, 16√2, 4√2. points: e(-1,4), l(-5,0)

Explanation:

Step1: Identify coordinates

Point \( E(-1, 4) \), Point \( L(-5, 0) \).

Step2: Apply distance formula

Distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
Substitute \( x_1 = -1, y_1 = 4, x_2 = -5, y_2 = 0 \):
\( d = \sqrt{(-5 - (-1))^2 + (0 - 4)^2} \)

Step3: Simplify inside radicals

\( -5 - (-1) = -4 \), \( 0 - 4 = -4 \)
\( d = \sqrt{(-4)^2 + (-4)^2} = \sqrt{16 + 16} \)

Step4: Combine and simplify

\( \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \)

Answer:

\( 4\sqrt{2} \) (corresponding to the option with \( 4\sqrt{2} \))