Assignment: The Line Segment and the Circle
Name:
Date:
Part 1: Communication
Answers to these questions are to be in full sentences and using the correct terminology. •
Be sure to state any formulas used.
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Answer in the space provided.
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To be handed in by the end of class
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1.
Explain 2 ways that you are able to prove mathematically that a figure is a right triangle if you are given only the coordinates of the vertices.
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2.
Explain using the mathematical process that you would use to classify a triangle as scalene, isosceles, or equilateral, using only the coordinates of the vertices.
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Given the endpoints of the diameter of a circle, explain two mathematical methods that you could use to determine the length of the radius. ______________________________________________________________________________________
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Part 2: Application
Full solutions for each of the following should be done in the space provided. •
Include diagrams where applicable
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Include all formula in a question.
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Pay attention to the method in which you present your answer. •
1.
An architect uses a grid for his design of a cottage. The diagram show a side view plan. The Architect knows that if any section of the roof is more than 9 units long, then additional rafters for support will be required.
Determine, mathematically, whether this roof will need additional support.
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2.
A quadrilateral has vertices P(2, 0), Q(4, 5),R(­1, 3) and S(­3, ­2). Determine, mathematically, what type of quadrilateral PQRS is. (i.e. rectangle, parallelogram, square, rhombus, kite) Use both slope and length formulas in you justification.
3.
AB is a line segment joining the points A(2, 3) and B(10, 3). Find the coordinates of the three points that divide AB into four equal parts.
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4.
Draw a diagram to represent each of the following problems. Determine the equation of the circle that models each problem. Show work to justify your solution.
a)
The rim of a bicycle wheel has a diameter of 69 cm.
b)
The shockwave from an earthquake travels outward in a circular pattern at a speed of 6 km/h. Model the shockwave 30 seconds after the start of the quake.
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c)
A rock is dropped into a pond and sends out a circular ripple. A toy boat is floating in the pond 4m east and 3m north of the spot where the rock was dropped. Find the equation of the ripple when it reaches the boat.
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