Question

find the distance between the points (2,3) and (5,5). round to three decimal places. distance =

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Here, \( x_1 = 2,y_1 = 3,x_2 = 5,y_2 = 5 \).

Step2: Substitute values into formula

Substitute the values: \( d=\sqrt{(5 - 2)^2+(5 - 3)^2}=\sqrt{3^2+2^2} \).

Step3: Simplify the expression

Calculate the squares: \( \sqrt{9 + 4}=\sqrt{13} \).

Step4: Compute the decimal value

\( \sqrt{13}\approx3.605551275 \). Round to three decimal places.

Answer:

\( 3.606 \)