Question

find the distance between the points. give an exact answer and an approximation to three decimal places.
(-4, -6) and (-1, -5)
the exact distance is
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( x_1 = -4 \), \( y_1 = -6 \), \( x_2 = -1 \), \( y_2 = -5 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1 = -1 - (-4) = -1 + 4 = 3 \)
\( y_2 - y_1 = -5 - (-6) = -5 + 6 = 1 \)

Then, substitute these into the distance formula:
\( d = \sqrt{(3)^2 + (1)^2} = \sqrt{9 + 1} = \sqrt{10} \)

Answer:

\(\sqrt{10}\)