We will get an acute angle if we draw a ray from the origin through a point in either quadrant I or quadrant IV. Let's mark the region in which the point can lie.
In this region the x-coordinate is a positive number and the y-coordinate is an arbitrary nonzero number. There are several ways we can combine the numbers given to us in the exercise to create such a point, say (1,2). This means that our solution is merely an example.
b Let's begin like we did in previous exercise, that is, we draw a ray from the origin through (4,0).
We now wish to create a right angle. The ray we see in the diagram is horizontal and therefore we need the second ray to be vertical. Our point must therefore lie on the y-axis.
To form a right angle, the x-coordinate must be 0 and the y-coordinate is an arbitrary nonzero number. The numbers that are given to us in the exercise we can combine in several different ways to create the point. Thus, (0,2) is just one possibility.
c Like before we begin by drawing the ray.
This time we wish to create an obtuse angle. We create such an angle by drawing a ray from the origin through a point which lies in quadrant II or quadrant III. Let's mark the region in which the point can lie.
We can see in the diagram that the x-coordinate must be a negative number and the y-coordinate can be any nonzero number. There are many combinations of the numbers in the exercise which create a point where we want it, (2,2) for instance, which is merely one possible solution.
d In the final exercise, we wish to create a straight angle. The ray we start with is the same we had in the previous three exercises.
To create a straight angle in the diagram we need to place the point on the x-axis left of the origin.
This means that the x-coordinate will be negative and the y-coordinate is 0. We can combine the given numbers in different ways to create such a point. One example is (- 2, 0).
