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2.5.3 Practice: Modeling: Wildlife Sanctuary Practice Geometry Honors Sem 2 Name Date YOUR ASSIGNMENT: Wildlife Sanctuary You are designing a path for traveling to one of the animal habitats in the wildlife sanctuary. Which of the following regions did you choose? Lion Habitat Hippo Habitat Elephant Habitat Make Sense of the Problem (3 Points: 1 Point for each answer) What do you know about the requirements for your two paths? What do you want to find out? What kind of answer do you expect?Making Sense of the Problem: Below is a graph that represents the wildlife sanctuary. The Crocodile River is represented by the liney = 4, and the center of each habitat is represented by a point. Analyze the Data: Path 1: You want path 1 to be a continuous distance of 1.5 km from the center of the habitat. 1. Path 1 represents what mathematical object? (1 point) 2. What is the radius of path 17 (1 point)3. Draw a rough sketch of path 1 on your graph. (1 point) 4. Will path 1 intercept the Crocodile River? (1 point) Use the Circle Tool on the activity page to help. 5. What is the maximum radius of path 1 before it intercepts the Crocodile River? Use the Circle Tool on the activity page to help. (1 point) Maximum radius = kmPath 2: You want path 2 to be equidistant from the Crocodile River and the habitat you chose. 6. Path 2 represents what mathematical object? (1 point) 7. What is the mathematical name for the object that is defined by the Crocodile River (1 point) 3. What is the mathematical name for the object that is defined by your selected region? (1 point)9. Draw a line that represents the shortest distance between your habitat's center point and the river. What is the midpoint of this line? (2 points) 10. This midpoint is the vertex (or bottom point) of your parabolic path. Draw the midpoint on your graph, then sketch the parabola that represents path 2. (1 point) Solving the Problem: Consider a point (x, y) that is on the path. Use the Parabola Tool on the activity page to help you visualize this point.11. Using the distance formula V(* - )'+ (:- m) find the distance from the benter of your habitat to the point (, y). Write this equation. Your answer will contain x- and y-terms. (1 point) 12. What is the distance from the directrix [the Crocodile River) to the point (xx)? Write this equation. Your answer will contain a y-term. (2 points) 13. Set these two distances equal to each other. (1 point)14. Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hind Square both sides to get rid of the square root Extending the Problem: The Serengeti Stream flows into the Crocodile River at the point (0, 4). The Serengeti Stream follows a straight-line path that goes through (6, 7), as shown.crocodile river 19 11 14 15. The zoo staff plans to put in a new road that is equidistant from the Serengeti Stream and the Crocodile River. Describe, using geometric terms, how that road is related to the Serengeti Stream and the Crocodile River. (1 point) 16. Write linear equations in slope-intercept form to model the Serengeti Stream and the Crocodile River. (4 points: 1 point for the equation for the Crocodile River, 3 points for the equation for the Serengeti Stream)17. Find the angle between the Crocodile River and the road. Show your work, and round your answer to the nearest tenth of a degree. (Hint Use trigonometry to help solve this problem.) (3 points) 18. Write an equation in slope-intercept form for the line the road will follow. (Hint: Again, use trigonometry to help you ) (2 points)