Question

use the map shown below to find the distance between cities a and b to the nearest tenth. the distance is (round to the nearest tenth as needed)

Explanation:

1. First, assume the coordinates of point A and point B:

• Let's assume the coordinates of point A are \((x_1,y_1)\) and the coordinates of point B are \((x_2,y_2)\) from the grid - based map. If we assume A is at the origin \((0,0)\) and B has coordinates \((6,4)\) (by observing the grid positions).
• The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) in a coordinate - plane is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

1. Then, substitute the values into the formula:

• Here, \(x_1 = 0,y_1 = 0,x_2 = 6,y_2 = 4\).
• Substitute these values into the distance formula: \(d=\sqrt{(6 - 0)^2+(4 - 0)^2}=\sqrt{6^{2}+4^{2}}=\sqrt{36 + 16}=\sqrt{52}\).

1. Next, simplify the square - root and round:

• We know that \(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx2\times3.606\approx7.2\).

Step1: Identify coordinates

Assume \(A(0,0)\), \(B(6,4)\)

Step2: Apply distance formula

\(d=\sqrt{(6 - 0)^2+(4 - 0)^2}=\sqrt{36 + 16}=\sqrt{52}\)

Step3: Simplify and round

\(d = 2\sqrt{13}\approx7.2\)

Answer:

7.2