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# 座標平面 (英): 座標平面

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- What we're going to do in this video is, through a bunch of
- examples, familiarize ourselves with the
- x,y-coordinate plane.
- And first we're going to just look at some points that are
- already plotted and figure out their coordinates.
- Then we're going to look at some coordinates and figure
- out where those points are.
- Then we'll do one more problem.
- So let's figure out what are the
- coordinates of these points?
- So you have this point right here, A.
- So its x-coordinate, you can see it right there.
- You just drop down.
- Where does it intersect the x-axis?
- x is equal to 5.
- So it's the point 5 comma and y is going to be equal to 6.
- 5 comma 6.
- Now this point B here, what's the x-coordinate?
- It is 5 to the left.
- 5 to the left of the x-axis.
- This is negative 5.
- Its x-coordinate is negative 5.
- y-coordinate is, if you just go straight to the right,
- you're going to hit y is equal to 5.
- y is equal 5.
- Let me switch colors.
- C.
- I think you're getting the hang of this.
- Let's do the y-coordinate first. The y-coordinate is 3.
- You see that right there.
- And then the x-coordinate is negative 2.
- Negative 2.
- You always put the x-coordinate first. That's
- just the convention we use.
- D, x-coordinate negative 2.
- You see that right there.
- y-coordinate negative 2, as well.
- Let me get another color.
- E, let's do the y-coordinate.
- We'll figure it out first, but you always
- have to write it second.
- It's negative 4.
- You see that right there, the y-coordinate.
- The x-coordinate is 3.
- And then finally, F.
- The x-coordinate is 2.
- And the y-coordinate is negative 6.
- Hopefully that gives you a sense of at least figuring out
- the coordinates.
- Now let's go the other way.
- Let's start with coordinates and figure out where those
- points are.
- So you have this first one.
- I'll do it lowercase case a in parentheses to differentiate
- it from this uppercase A.
- So it's at 4 comma 2. x is equal to 4.
- y is equal to 2.
- So that's that point right there.
- Let's do the next one.
- Let me do it in a color that you'll be able to read.
- b.
- x is equal to negative 3.
- y is equal to 5.5.
- So you go all the way up to 5.5.
- y is equal to 5.5.
- So that is the point lowercase b with parentheses around it.
- Then c, 4 negative 4. x is equal to 4.
- y is equal to negative 4.
- Right over there.
- And then one last one.
- I'll do it in orange.
- d, x is negative 2, y is negative 3.
- Right there.
- That's the d with parentheses.
- And you could have gone the other way.
- You could have said, hey, y is equal to negative 3.
- x is equal to negative 2.
- So you could go to the left and down.
- Or you could go down and to the left.
- And you're still going to get to the same point.
- So hopefully that gives you a good sense of how to figure
- out coordinates.
- Or if you're given coordinates, how to figure out
- where to plot something on the x,y-coordinate plane.
- Now let's do a slightly more involved problem.
- So it says the following 3 points are 3 vertices of
- square A, B, C, D.
- Plot them on a graph.
- Then determine what the coordinates of the fourth
- point, D, would be.
- All right, let's plot these on a graph, as
- they tell us to do.
- All right.
- That'll be my y-axis.
- That's my y-axis.
- The vertical axis.
- That'll be my x-axis.
- And let me put some-- let me mark it.
- So that's x equals 1, 2, 3, 4.
- This is x is equal to negative 1, negative 2, negative 3,
- negative 4.
- That's y is equal to 1, 2, 3, 4.
- This is y is equal to negative 1, negative 2, negative 3,
- negative 4.
- I could write that this y equals 4.
- This y equals negative 4. x is equal to 4.
- x is equal to negative 4.
- And let's see.
- Let's plot these points.
- So first, we have the point A is equal to negative 4,
- negative 4.
- So we go x is negative 4.
- And then y is negative 4.
- So we drop down 4 right there.
- And that is our point A.
- Negative 4, negative 4.
- And just to familiarize yourself with a labeling
- scheme that you may or may not have seen before, is that
- people label these sections of the coordinate plane.
- They call this the first quadrant.
- They call this the second quadrant.
- They call this the third quadrant.
- And they call this the fourth quadrant.
- And these are just the Roman numerals for I, II, III, and
- IV, So this point is in the third quadrant.
- When we looked up at this stuff over here, these points
- are in the fourth quadrant.
- These are in the third, second, first. Just an
- interesting thing to know.
- Sometimes someone might ask you, what quadrant
- is that point in?
- And you just say, OK, I see.
- If they're both negative, they're going to be in the
- third quadrant.
- If just the y is negative, but the x is positive, you're
- going to be in the fourth.
- If they're both positive, you're in the first. If y is
- positive, but x is negative, you're in the second.
- And we'll talk a little bit about that as
- we plot these points.
- So point B, x is positive.
- It's 1, 2, 3.
- And y is negative 4.
- So we drop down here into the fourth quadrant.
- That is the point B.
- It's 3, negative 4.
- So we can already see the bottom of our rectangle that
- they're talking about, right there.
- And notice, both of these have the exact same y.
- They're both at the same level below the x-axis.
- And then what's the next point?
- Point C is 3 comma 3.
- So 3 comma 3.
- It's in the first quadrant.
- Both of its coordinates are positive.
- 3 comma 3.
- Both x and y are positive.
- And notice, it's on the same vertical as B.
- It has the same x value.
- They both have an x value of 3.
- So it's right above it.
- Right above it.
- Now we have to figure out the last point here.
- Well, the point is going to have to be on the same
- vertical as this point.
- It's going to have to be on the same vertical as this
- point, which means it's going to have the same x value as
- this point.
- So its x value is going to be negative 4.
- And then it's going to have to be on the same horizontal as
- this point.
- It's going to have to be on the same
- horizontal as that point.
- So it's going to have to have the same y value at the same
- height above the x-axis.
- So it's going to have to be 3.
- So that is our point D.
- Notice it's at negative 4, right above A.
- And it's at y is equal to 3.
- Right to the left of point C.
- And we are done.

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