54.7k views
1 vote
John was visiting four cities that form a rectangle on a coordinate grid at A(0,4), B(4,1), C(3,-1) and D(-1,2). If he visited all the cities in order and ended upwhere he started, what is the distance he traveled? Round your answer to thenearest tenth.

1 Answer

0 votes

The total distance John travelled can be obtained by finding the sum of the distances between two consequtive points.

The expression for the distance between two points is,


D=\sqrt[]{(x_2-x_1)^2+(y^2-y_1)^2}

Here, (x1, y1) and (x2,y2) are the coordinates of two points.

Given, A(0,4), B(4,1), C(3,-1) and D(-1,2) are the coordinates of cities.

The distance beween A(0,4) and B(4,1) is,


\begin{gathered} AB=\sqrt[]{(4-0)^2+(1-4)^2} \\ =\sqrt[]{16+(-3)^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5 \end{gathered}

The distance beween B(4,1) and C(3,-1) is,


\begin{gathered} BC=\sqrt[]{(3-4)^2+(-1-1)^2} \\ =\sqrt[]{(-1)^2+(-2)^2} \\ =\sqrt[]{1+4} \\ =\sqrt[]{5} \end{gathered}

The distance beween C(3,-1) and D(-1,2) is,


\begin{gathered} CD=\sqrt[]{(-1-3)^2+(2-(-1)})^2 \\ =\sqrt[]{(-4)^2+3^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5 \end{gathered}

The distance beween A(0,4) and D(-1,2) is,


\begin{gathered} AD=\sqrt[]{(-1-0)^2+(2-4)^2} \\ =\sqrt[]{1+(-2)^2} \\ =\sqrt[]{1+4} \\ =\sqrt[]{5} \end{gathered}

Now, the total distance John traveled is,


\begin{gathered} D=AB+BC+CD+AD \\ =5+\sqrt[]{5}+5+\sqrt[]{5} \\ =10+2\sqrt[]{5} \\ =14.5 \end{gathered}

Therefore, the total distance John traveled rounded to the nearest tenth is 14.5 units.

User NinjaCross
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories