Question

if each unit on the grid represents 1 kilometer, rhea traveled km. round to the nearest kilometer, if necessary

Explanation:

1. First, find the coordinates of the points:

• Assume the coordinates of point \(X=(0,2)\), point \(Y=(2,6)\), and point \(Z=(9,2)\).
• Use the distance - formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the lengths of the sides of the triangle (the path of travel).
• Calculate the distance between \(X(0,2)\) and \(Y(2,6)\):
• Let \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(2,6)\).
• \(d_{XY}=\sqrt{(2 - 0)^2+(6 - 2)^2}=\sqrt{2^2+4^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47\) km.
• Calculate the distance between \(Y(2,6)\) and \(Z(9,2)\):
• Let \((x_1,y_1)=(2,6)\) and \((x_2,y_2)=(9,2)\).
• \(d_{YZ}=\sqrt{(9 - 2)^2+(2 - 6)^2}=\sqrt{7^2+( - 4)^2}=\sqrt{49 + 16}=\sqrt{65}\approx8.06\) km.
• Calculate the distance between \(Z(9,2)\) and \(X(0,2)\):
• Let \((x_1,y_1)=(9,2)\) and \((x_2,y_2)=(0,2)\).
• \(d_{ZX}=\sqrt{(0 - 9)^2+(2 - 2)^2}=\sqrt{( - 9)^2+0^2}=9\) km.

1. Then, find the total distance traveled:

• The total distance \(D=d_{XY}+d_{YZ}+d_{ZX}\).
• \(D\approx4.47 + 8.06+9\).
• \(D\approx21.53\approx22\) km.

Answer:

22