Question

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

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = 6,y_1=9,x_2=-3,y_2 = 7\).

Step2: Substitute the values

Substitute the values into the formula: \((x_2 - x_1)=-3 - 6=-9\), \((y_2 - y_1)=7 - 9=-2\). Then \(d=\sqrt{(-9)^2+(-2)^2}\).

Step3: Calculate the squares

\((-9)^2 = 81\), \((-2)^2=4\). So \(d=\sqrt{81 + 4}\).

Step4: Sum and simplify

\(81+4 = 85\), and \(\sqrt{85}\) cannot be simplified further.

Answer:

\(\sqrt{85}\)