Question

question 9 (3 points) modeling real life park officials want to build a boardwalk that passes a geyser. a proposed design is shown. the boardwalk must be at least 100 feet from the center of the geyser at point gg. does the design meet this requirement? first, find the distance from g to h to the nearest tenth. this distance is __ units. next, each unit on the diagram = 15 feet. how many feet does this represent? feet finally, does this design meet the requirement (yes or no)? __

Explanation:

Step1: Calculate the distance between G(3,9) and H(6,3) using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Here \(x_1 = 3,y_1=9,x_2 = 6,y_2 = 3\).
\(d=\sqrt{(6 - 3)^2+(3 - 9)^2}=\sqrt{3^2+(- 6)^2}=\sqrt{9 + 36}=\sqrt{45}\approx6.7\) units.

Step2: Convert the distance from units to feet

Since 1 unit = 15 feet, then the distance in feet is \(d_{feet}=6.7\times15 = 100.5\) feet.

Answer:

6.7 units; 100.5 feet; yes