Main content

## Distance on the coordinate plane

## Video transcript

Milena's town is built
on a grid similar to the coordinate plane. She is riding her bicycle
from her home at point negative 3, 4 to the mall at
point negative 3, negative 7. Each unit on the graph
denotes one city block. Plot the two points,
and find the distance between Milena's
home and the mall. So let's see, she's
riding her bicycle from her home at the
point negative 3, 4. So let's plot negative 3, 4. So I'll use this
point right over here. So negative 3 is
our x-coordinate. So we're going to go 3 to the
left of the origin 1, 2, 3. That gets us a negative 3. And positive 4 is
our y-coordinate. So we're going to go
4 above the origin. Or I should say, we're
going to go 4 up. So we went negative 3,
or we went 3 to the left. That's negative 3, positive 4. Or you could say we went
positive 4, negative 3. This tells us what we do in
the horizontal direction. This tells us what we do
in the vertical direction. That's where her home is. Now let's figure out
where the mall is. It's at the point
negative 3, negative 7. So negative 3, we
went negative 3 along the horizontal
direction and then negative 7 along the vertical direction. So we get to negative 3,
negative 7 right over there. And now we need to
figure out the distance between her home and the mall. Now, we could
actually count it out, or we could just compute it. If we wanted to count it out,
it's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 blocks. So we could type that in. And another way to
think about it is they have the exact
same x-coordinate. They're both at the
x-coordinate negative 3. The only difference
between these two is what is happening
in the y-coordinate. This is at a positive 4. This is at a negative 7. Positive 4, negative 7. So we're really trying to
find the distance between 4 and negative 7. So if I were to say
4 minus negative 7, we would get this
distance right over here. So we have 4 minus negative 7,
which is the same thing as 4 plus 7, which is 11. Let's do a couple more. Carlos is hanging a
poster in the area shown by the red rectangle. He is placing a nail in the
center of the blue line. In the second graph, plot the
point where he places the nail. So he wants to place a nail in
the center of the blue line. The blue line is 6 units long. The center is right over here. That's 3 to the
right, 3 to the left. So he wants to put the nail
at the point x equals 0, y is equal to 4. So he wants to put it at x is
equal to 0, y is equal to 4. That's this point
right over here. So let's check our answer. Let's do one more. Town A and Town B are
connected by a train that has a station at the
point negative 1, 3. I see that. The train tracks are in blue. Fair enough. Which town is closer to
the station along the train route, Town A or Town B? So they're not just
asking us what's the kind of crow's
flight, the distance that if you were to fly. They're saying,
which town is closer to the station along
the train route? So if you were to follow the
train route just like that. So the A right over here, A if
you were going along the train route, you would have
to go 1, 2, 3, 4, 5, 6 in the x-direction,
and then 1, 2, 3, 4, 5 along the y-direction. So you'd have to
go a total of 11. If you're going from B, you're
going 1, 2, 3, 4, 5, 6, 7, 8 9, 10, 11 along the
x-direction, and then 1, 2, 3, 4, 5, 6, so 6 along
the vertical direction. So you're going
to go a total 17. So it's pretty obvious that
A is closer along the tracks. Now, you could also think about
it in terms of coordinates because A is at the
coordinate of negative 7, 8. And if you were to think
about negative 7, 8, to get from negative
7 to negative 1 along the x-coordinate,
you're going to go 6. And then to go from 8 to 3,
you're going to go 5 more. So you could also not
necessarily count it out, you can actually just think
about the coordinates. But either way, you see
that town A is closer.