Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the coordinates

From the graph, the first point is at \((0, -1)\) (on the y - axis, 1 unit below the origin) and the second point is at \((2, -5)\) (2 units to the right on the x - axis and 5 units below the origin).

Step2: Apply the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute \(x_1 = 0,y_1=-1,x_2 = 2,y_2=-5\) into the formula:
\[

$$\begin{align*} d&=\sqrt{(2 - 0)^2+(-5-(-1))^2}\\ &=\sqrt{(2)^2+(-5 + 1)^2}\\ &=\sqrt{4+(-4)^2}\\ &=\sqrt{4 + 16}\\ &=\sqrt{20}\\ &=\sqrt{4\times5}\\ &= 2\sqrt{5} \end{align*}$$

\]

Answer:

\(2\sqrt{5}\)