Question

find the distance between the pair points (3,2) and (6,8)

Explanation:

Step1: Recall 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, \(x_1 = 3,y_1=2,x_2 = 6,y_2 = 8\).

Step2: Substitute the values into the formula

First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
\(x_2 - x_1=6 - 3=3\)
\(y_2 - y_1=8 - 2=6\)
Then, \((x_2 - x_1)^2+(y_2 - y_1)^2=3^2+6^2=9 + 36=45\)

Step3: Calculate the square - root

\(d=\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx3\times2.24 = 6.72\)

Answer:

The distance between the points \((3,2)\) and \((6,8)\) is \(3\sqrt{5}\approx6.72\)