Question

question
find the distance between the two points in simplest radical form.
$(6,9)$ and $(-3,7)$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(6,9)\) and \((x_2,y_2)=(-3,7)\)

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

Substitute the values: \(d=\sqrt{(-3 - 6)^2+(7 - 9)^2}\)

Step3: Simplify the expressions inside the square - root

\(-3-6=-9\), \(7 - 9=-2\)
\(d=\sqrt{(-9)^2+(-2)^2}=\sqrt{81 + 4}\)

Step4: Calculate the sum

\(81+4 = 85\)
\(d=\sqrt{85}\)

Answer:

\(\sqrt{85}\)