Concept Check The two methods of expressing bearing can be interp...

Question

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods.

(0, -2)

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the bearing of an object located at the point represented by the coordinates given our given coordinates are zero negative five. Our answer choices are answer choice. A 180 degrees answer choice B south, zero degrees west. Answer choice C east 90 degrees south and answer choice D both A and B. All right. First, let's determine where this object is located on a coordinate plane. We'll draw a vertical Y axis in a horizontal X axis. They come together at the origin in the middle. Now, for our coordinates zero, negative five, we know from previous lessons that the X value is given first and the Y value is given second, our X value is zero. So from the origin, we move neither left nor right. For an X value of zero, for A Y value of negative five. From the origin, we're going to move down five units. So we can label this as zero, negative five. But for bearing, it's not so important that we have units labeled as we know in what direction our object is located. We know that when we're talking about bearing, our coordinate plane becomes like a compass and north is going to be the positive part of the Y axis. And then we have yeast is going to be the positive part of the X axis. South is going to be the negative part of the Y axis and west is going to be the negative part of the X axis. And we recall from previous lessons and from the textbook that the bearing can be described in two different ways. The first way is to just give us an angle measurement. Now, when we have an angle measurement, we're always going to start with do north. So that initial side of our angle is going to be pointing north up toward the positive part of the X or the y axis, excuse me up toward the positive part of the y axis. And then we are going to move clockwise however many degrees were told. Now, if we are moving clockwise from due north and we want to pass through that 0.0 negative five, we're going to go down 180 degrees. So we have one way to express the bearing here is 180 degrees. Now, the other way to express bearing is we can start due north or south. We can only start north or south, but we can start either north or south and then we head however many degrees east or west. So here we could start south because that zero, negative five is south. And then, so we can draw our initial side along the negative part of the Y axis. And then, because we are right on that negative part of the Y axis, we're moving zero degrees west or, and zero degrees east. Two ways to express that is we start south and we go zero degrees west and then south, zero degrees east. So all of those would be acceptable answers for describing the bearing of this object. Now, let's look at our answer choices. Answer choice A is the 180 degrees. So that first method, so answer choice A works answer choice B is south zero degrees west. That's another acceptable answer. So answer choices A and B work so far answer choice C begins at east. Well, you can't do that. You have to begin with north or south. So answer choice C does not work. Therefore, answer choice D which says both A and B is the correct answer. Well done. We'll catch you on the next one.

Key Concepts

Bearing

Rectangular Coordinate System

Conversion of Coordinates to Bearings

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