WEBVTT
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The grid shows the points 𝐴 and 𝐵.
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Part a) State the coordinates of the point 𝐵.
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Part b) On the grid, mark with a cross a point 𝐶, such that 𝐴𝐵𝐶 is a right-angled isosceles triangle.
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Part c) On the grid, mark with a cross the point three, one.
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Label this point 𝐷.
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So the first thing we’re interested in is point 𝐵 because we want to find the coordinates of point 𝐵.
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And whenever we’re trying to find the coordinates of a point, we always start with the 𝑥-coordinate.
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So actually, we can also say that it’s along the corridor.
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So we do along the corridor then up the stairs or downstairs.
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That’s one way of remembering to do 𝑥-coordinate, then 𝑦-coordinate.
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We can see here the 𝑥-coordinate is actually at 𝐴 cause we go along from zero to eight.
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And we can see that actually the point 𝐵 is up from there.
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And then, we move on to our 𝑦-coordinate.
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And we can see here that the coordinate is going to be three and that’s because we go from zero up to three.
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And we can see that along, we’d actually see that 𝐵 is at this point.
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So therefore, we could say that the coordinates at the point 𝐵 are going to be eight, three.
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Okay, now, let’s move on to part b.
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In part b, we need to draw our point 𝐶 such that 𝐴𝐵𝐶 is a right-angled isosceles triangle.
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So the key thing here is “what is a right-angled isosceles triangle?”
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Well, here, I’ve drawn a little sketch to help us understand.
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So a right-angled isosceles triangle is a triangle with a right angle; seeing this arrow pointing at here.
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And also, it has two identical sides and we see those with these little lines here cause that’s what it means; it means these sides are the same.
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And then, we’d also have two angles.
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So our two base angles here would also be the same.
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So this is a right-angled isosceles triangle.
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So now, let’s draw a one on our grid.
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Well, actually, I’m gonna show these three places where we could actually put point 𝐶 so that 𝐴𝐵𝐶 is actually a right-angled isosceles triangle.
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So the first where we’re gonna have a look at is to have a right angle at 𝐴.
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So in order for it to be a right-angled isosceles triangle, what we need to do is have two sides which are actually the same length.
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So we’ve got 𝐴𝐵, which is six units.
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So therefore, we’ve actually placed the point 𝐶 six units away from point 𝐴.
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So therefore, we can say that 𝐶𝐴 is six units long or six squares.
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So now, you can see that we’ve actually answered the question because we’ve got a point 𝐶 and it’s at the coordinates two, nine, where the triangle 𝐴𝐵𝐶 is a right-angled isosceles triangle.
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And that’s because we have two sides of the same length and a right angle.
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Okay, so now, let’s look at the other two possibilities for where 𝐶 could go.
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Well, the next possibility is to have the right angle at point 𝐵.
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Again, 𝐴𝐵 is six units long.
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So we’ve placed the point 𝐶 six units away or six squares away from point 𝐵.
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So we can say that 𝐶𝐵 is six units long now.
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So therefore, the point two, three is another possible point for point 𝐶 because we’ve now drawn again another right-angled isosceles triangle.
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Okay, so now, let’s move on to our last point.
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Now, for our last possible point, we actually want the right angle to be away from 𝐴 or 𝐵.
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And the only way for that to happen would be to have the angles at 𝐴 and 𝐵 as 45 degrees.
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So here, we can use the grid squares to help us because we can actually go out from 𝐵 and 𝐴 at a diagonal.
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So therefore, we know it’ll be 45 degrees because we’re dealing with squares.
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And we can actually go three squares diagonally out.
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And we can actually see we get to the new point 𝐶 at five, six cause that creates a right angle.
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And we also have two identical sides.
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So we’ve answered part b.
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We’ve actually drawn three points such that 𝐴𝐵𝐶 could be a right-angled isosceles triangle.
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So finally, part c, what we need to do is actually mark on the grid the point three, one.
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Well, we already know from earlier that when we’re looking at coordinates, the first coordinate is our 𝑥-coordinate and then the second coordinate will be our 𝑦-coordinate.
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So we know three will be our 𝑥-coordinate and one will be our 𝑦-coordinate.
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So I’ve actually marked these on our 𝑥- and 𝑦-coordinates.
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So we got three and one.
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We can see that where these points meet is going to be the point 𝐷 at the coordinates three, one.
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So we’ve answered part c as we’ve marked on the grid with a cross the point three, one.