Question

1. max threw a frisbee to sam along the path shown below. determine the distance the frisbee traveled. round to the nearest tenth, if needed.

Explanation:

1. First, assume the coordinates of Sam and Max:

• Let's assume Sam's position has coordinates \((x_1,y_1)\) and Max's position has coordinates \((x_2,y_2)\) by looking at the grid - if we assume each square of the grid is 1 unit. Suppose Sam is at \((- 8,7)\) and Max is at \((2,-4)\).
• 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, \(x_1=-8,y_1 = 7,x_2 = 2,y_2=-4\).
• First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
• \(x_2 - x_1=2-(-8)=2 + 8 = 10\).
• \(y_2 - y_1=-4 - 7=-11\).
• Then, calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\):
• \((x_2 - x_1)^2+(y_2 - y_1)^2=10^2+(-11)^2=100 + 121=221\).
• Now, find the distance \(d\):
• \(d=\sqrt{221}\approx14.9\).

Step1: Identify the distance formula

The formula for distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Determine the coordinates

Assume Sam at \((-8,7)\) and Max at \((2,-4)\).

Step3: Calculate differences in coordinates

\(x_2 - x_1=2-(-8)=10\) and \(y_2 - y_1=-4 - 7=-11\).

Step4: Calculate the sum of squared differences

\((x_2 - x_1)^2+(y_2 - y_1)^2=10^2+(-11)^2 = 100+121 = 221\).

Step5: Calculate the distance

\(d=\sqrt{221}\approx14.9\).

Answer:

14.9