Question

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

Explanation:

Step1: Identify the coordinates

First, we need to find the coordinates of the two points. From the graph, one point is at \((0, 5)\) (on the y - axis, x = 0, y = 5) and the other point is at \((-1, -1)\) (x=-1, y = - 1).

Step2: Apply the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Let \((x_1,y_1)=(0,5)\) and \((x_2,y_2)=(-1,-1)\).
Substitute the values into the formula:
\(x_2 - x_1=-1 - 0=-1\)
\(y_2 - y_1=-1 - 5=-6\)
Then \(d=\sqrt{(-1)^2+(-6)^2}=\sqrt{1 + 36}=\sqrt{37}\)

Answer:

\(\sqrt{37}\)