Question

find the distance between the two points rounding to the nearest tenth (if necessary). (6,8) and (8,6)

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 \(x_1 = 6,y_1 = 8,x_2 = 8,y_2 = 6\).

Step2: Substitute the values into the formula

Substitute the values: \(d=\sqrt{(8 - 6)^2+(6 - 8)^2}=\sqrt{2^2+(- 2)^2}\).

Step3: Simplify the expression inside the square - root

Calculate \(2^2+(-2)^2\): \(2^2 = 4\), \((-2)^2=4\), so \(2^2+(-2)^2=4 + 4=8\). Then \(d=\sqrt{8}\).

Step4: Calculate the square - root and round

\(\sqrt{8}\approx2.828\). Rounding to the nearest tenth, \(d\approx2.8\).

Answer:

\(2.8\)