Science:Math Exam Resources/Courses/MATH152/April 2017/Question A 11
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Question A 11 

Let and . Sketch the set of points on the graph below. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Observe that can be written as . What point is this when ? How about when ? And when ? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The location of can be thought of as the endpoint of the vector sum of and as shown below. Notice that is a scaled version of , and since , its length ranges between 0 and the full length of . Hence the set in question is simply a line segment between and : 