Question

find the distance between the two points in simplest radical form.
answer attempt 2 out of 2

Explanation:

Step1: Identify the coordinates of the two points

From the graph, the two points are \((-6,5)\) and \((-3,-3)\). Let \((x_1,y_1)=(-6,5)\) and \((x_2,y_2)=(-3,-3)\).

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(x_2 - x_1=-3-(-6)=-3 + 6 = 3\), \(y_2 - y_1=-3 - 5=-8\).
Then \(d=\sqrt{(3)^2+(-8)^2}\).

Step3: Calculate the squares and sum

\((3)^2 = 9\), \((-8)^2=64\). So \(d=\sqrt{9 + 64}\).

Step4: Simplify the radical

\(9+64 = 73\), so \(d=\sqrt{73}\).

Answer:

\(\sqrt{73}\)