Dimensions of rectangle from coordinates example

- [Voiceover] Rectangle ABCD is graphed

in the coordinate plane.

The following are the
vertices of the rectangle,

and they give us the labels
for the vertices as well.

Given these coordinates,
what is the length

of side AD of this rectangle?

So let's just plot it.

That's one way that we could tackle it.

So let's, let me see,
all of these are actually

in the first coordinate,

so I could focus on the first coordinate.

So let's say that's my y-axis.

It's my y-axis, and let me draw my x-axis.

My x-axis, and actually
I wanna really focus in

on the points A and D,

because we just need to
find the length of the side

from point A to point D.

So point A, let me do
this in another color.

So point A is at x equals seven,

y is equal to one.

So one, two, three, four,

five, six, seven, so
that's x equals seven.

Y is equal to one.

Y is equal to one, so that
is point A right over there.

Point A, let me label it. Point A.

And then where's point D?

Point D has the exact same x-coordinate,

but its y-coordinate
is a little bit higher.

Its y-coordinate is six.
It's actually five higher.

So point D is at x equals seven,

y is equal to six.

So y is equal to one, two, three,

four, five, and six.

So that's y is equal to six,

and so we can draw the point.

It is going to be right over here.

This is point D,

and we could actually connect
them with a line, if we like,

to show that this is
a side of a rectangle.

Let me draw that. I can
just draw this like this.

And there you have it.

I haven't even drawn
the whole rectangle yet,

but just by plotting these two points,

we can think about how long side AD is.

We could say, look, the x
doesn't change going from A to D,

but we do increase in
the y direction by five.

We go from y is equal to
one to y is equal to five,

to y is equal to six.

So our change in y is equal to five.

So what's the length of this line?

Well, it's gonna be five.

It's gonna be five,
whatever the units are.

So that's the length of side AD.

It's going to be equal to five.

We went from the point (7, 1)

to the point (7, 6).

Now, they said that this was a rectangle.

Now, just for our satisfaction,

we can draw the entire rectangle.

We have that point B
that is at x equals five,

y is equal to one, so let me draw that.

And I'm just doing this just
for fun now at this point.

We're done with the problem.

So x equals five, y equals
one. That's right over here.

That's point B.

Let me write B. That's the point (5, 1).

And then we have the point C.
I'll do this in another color.

The point C is at x
equals five, y equals six.

X equals five, y equals six.

Point C is right over here.

Point C is the point x equals
five, y is equal to six.

And then we could connect
all the dots, if we like,

and clearly see that it is a rectangle.

So I could connect those.

I could connect these two.

Then I could connect these two.

And then we see that we
indeed have a rectangle.

But we answered it awhile
ago that the length

of side AD is equal to five.

If we cared about the other sides,

the length of BA, well, this is two.

a difference of two along the x direction,

the horizontal direction,

difference of two along the x direction,

difference of five in the y direction.

We go from y equals one to y equals six.

So there you have it.

We actually will figure
out all of the dimensions

of this rectangle.