Video Transcript
Use the graph below to determine
the points 𝐴, 𝐵, 𝐶, and 𝐷 and find the area of the shape that results from
connecting them.
So the first thing we’re gonna do
in this question is find the coordinates of our points 𝐴, 𝐵, 𝐶, and 𝐷. So what we’re gonna do is take a
look at 𝐴 first. Now, if we want to find the
coordinates of a point, what we look at first is the 𝑥-coordinate and then we look
at the 𝑦-coordinate. And sometimes this is known as
going along the corridor and up the stairs. So for 𝐴, we can see that our
𝑥-coordinate is going to be negative four because that’s where 𝐴 lies on the
𝑥-axis. And our 𝑦-coordinate is going to
be six. So, that means the coordinate
points of 𝐴 are negative four, six. Okay, great! So now we can use the same method
to find the coordinates of 𝐵, 𝐶, and 𝐷.
Well, point 𝐵 is gonna be negative
four, negative six. Point 𝐶 is gonna be four, negative
six. And point 𝐷 is gonna be four,
six. So therefore, we’ve solved the
first part of the problem because what we’ve done is we’ve determined the
coordinates of points 𝐴, 𝐵, 𝐶, and 𝐷. So now what we want to do is find
the area of the shape that results from connecting them. So, now what we’ve done is we’ve
actually connected the points to make our shape. But what shape is it? And what we have, in fact, is a
rectangle, and we know that’s a rectangle because we know that the pairs of sides
are, in fact, parallel.
And we know that because if we look
at our coordinates of our points, we can see, for example, that 𝐴 and 𝐵 have the
same 𝑥-coordinate, 𝐵 and 𝐶 have the same 𝑦-coordinate, 𝐶 and 𝐷 have the same
𝑥-coordinate, and 𝐴 and 𝐷 have the same 𝑦-coordinate. So therefore, we have our
rectangle. Well, we know that the area of a
rectangle can be found by multiplying the length and the width. Well, first of all, we can see that
the width of our rectangle is eight units, and we can get that by counting the
squares along.
Or we could have also found the
width of our rectangle by finding the difference between the 𝑥-coordinates of 𝐴
and 𝐷. So we’d have four minus negative
four. I also here put the modulus or
absolute value sign around because what we’re looking at is the magnitude because if
we’re trying to find length, we’re only interested in positive value. And this would give us eight
because four minus negative four, if you subtract a negative, it’s the same as
adding a positive.
Well, now we can find the length of
the rectangle. We could do this again with two
ways. One, we could count the squares,
and we could see that it’s 12 units long. Or again, we could find the
difference in the 𝑦-coordinates, this time, of 𝐷 and 𝐶. Well, what we’d have is negative
six, because that’s the 𝑦-coordinate of 𝐶, minus six, which would give us negative
12. But as we already said, we’ve got
the modulus or absolute value here because all we’re interested in is the magnitude
because we want to find the length of the side. And the modulus of negative 12 is
just 12, so the area is gonna be equal to 12 multiplied by eight, which is gonna
give us 96 square units.
