On the last Sunday of August every year, 1700+ athletes rush into the waters of Lake Okanagon in Penticton, B.C.. They are partaking in one of the most grueling sporting events in the world, the Ironman Canada Triathlon. During this event athletes will swim, bike and run various distances. The winners will complete the race in just over 8 hours, while some of the slower participants will use all of the designated 17 hours.

Coordinate Geometry is a useful tool to explore the three different courses that athletes will complete during their day.

SWIM COURSE

Assuming that the swim starts on the beach at the coordinates (0,0) of an imaginary grid system, plot the swim course and answer the following questions:

1. At the start, swimmers enter the water and swim in a straight line towards the houseboat located at coordinates (-0.5,1.2). How far have they swum and what is the equation of the line they followed?
2. At the houseboat swimmers turn 90 degrees to the right and swim to a large orange buoy located at coordinates (0.2, 1.49). What is the slope of the second leg of the swim course? How far have they traveled so far?
3. Once at the buoy, the swimmers have a third and final leg to swim. The finish line is located on the beach but to the right of the start line. The finish line is located at coordinates (.2, 0). What is the equation of the last leg of the swim course? What is the total distance of the swim course?

BIKE COURSE

Out of the water, athletes strip off their wet suits and rush through a change tent to put on their biking clothes. They hop on their bikes and head out onto the exhausting 180-km bike course. Answer the following questions using the profile provided.

1. There are 20 different legs shown on the profile. Find the equation of three of those legs. Are any of the three legs you chose parallel? Are any of the three legs you chose perpendicular? How do you know?
2. Photographers wait for the cyclists at a point half way through the steepest uphill leg. It is easiest to snap a photo when cyclists are moving at a lower speed. What are the coordinates of the photographers?
3. There is a crucial aid station at the midpoint of leg O; this is where athletes pick up much needed food, Gatorade and water. There is also a massage therapist there to help athletes work out any muscle cramps that may have formed over the last 5 - 7 hours of physical exertion. What are the coordinates of this aid station?

RUN COURSE

It is very important for an official Ironman race to be exactly the correct length. If the course were not the official distance then the athletes would not be able to qualify for the Ironman World Championships held every October in Kona, Hawaii. Explain in words how could you use coordinate geometry to calculate the distance of the 42.2-km marathon course? List at least five key points/ideas that would accurately measure the course distance.

IMC bike course profile

IMC run course map