### Video Transcript

The coordinate Plane: First
Quadrant

In this video, we will learn how to
find the ๐ฅ- and ๐ฆ-coordinates of a point in the first quadrant and locate a point
given its coordinates.

The coordinate plane is formed by a
horizontal number line called the ๐ฅ-axis and a vertical number line called the
๐ฆ-axis. Each axis crosses each other at
zero. The axis or the coordinate plane is
divided into four sectors, which are called quadrants. This sector is called the first
quadrant.

An ordered pair describes the
location of a point on the coordinate plane. The first number is called the
๐ฅ-coordinate, and the second number is called the ๐ฆ-coordinate. So, the coordinates for the pink
point marked on our coordinate plane are three, three. Letโs take a closer look at some
coordinates.

Here we go. Our coordinate plane is made up of
a horizontal number line called the ๐ฅ-axis and a vertical number line called the
๐ฆ-axis. And we know that each axis crosses
each other at zero. And we know that an ordered pair
describes the location of a point on the coordinate plane. We always write the ๐ฅ-coordinate
first, followed by the ๐ฆ.

Did you notice all the points that
have appeared on our coordinate plane? These points can be joined to make
a picture. I wonder if you can work out what
it is? Weโve joined some of the
points. Can you tell what it is yet? I bet you can tell what it is
now. Now that weโve ready to tell you
must have spotted that this is a dog. Letโs use some coordinates to give
our dog an eye and a nose. This is where weโre going to draw
our nose using a black circle.

The ๐ฅ-coordinate is always the
first number in our ordered pair. If we draw a line from our point
down to the ๐ฅ-axis, we can see the coordinate is one. And if we do the same with the
๐ฆ-axis, join our point along to the axis, we can see that the ๐ฆ-coordinate is
seven. So, letโs draw on our nose at one,
seven. There we go.

Now, weโve got an eye. What are the coordinates for our
dogโs eye? Letโs start by drawing a line from
our point down to the ๐ฅ-axis. Here we go, which is number
three. So, we know our ๐ฅ-coordinate is
three. Now, we need to draw a line from
our point to the ๐ฆ-axis. It reaches number seven. So, the coordinates, or the ordered
pair, for our dogโs eye are three, seven. Letโs practice using coordinates
now by answering some questions.

What is the ๐ฅ-coordinate of
point ๐ด?

In this question, we have to
write one of the coordinates for point ๐ด. We write coordinates as an
ordered pair. We usually write the
๐ฅ-coordinate first. This number line is called the
๐ฅ-axis. This is the coordinate which we
have to find. So, letโs draw a line from our
point, point ๐ด, all the way down to the ๐ฅ-axis. Here we go, starting at ๐ด all
the way down to the ๐ฅ-axis. Our arrow is pointing to number
three. So, the ๐ฅ coordinate of point
๐ด is three.

Write the ordered pair for the
location of the monkeys.

In this question, we have to
locate the monkeys on the coordinate plane. Here they are. Weโve marked them with the pink
dot. Now, we have to write the
ordered pair. An ordered pair describes the
location of a point on the coordinate plane. The first number is called the
๐ฅ-coordinate, and the second number is called the ๐ฆ-coordinate. So, letโs start by locating the
๐ฅ-coordinate. To do this, we can draw a line
from our point down to the ๐ฅ-axis.

Now, we can see the
๐ฅ-coordinate is four, and we can do the same to find the ๐ฆ-coordinate. We start at our point and draw
a line across to the ๐ฆ-axis. Now, we can see our
๐ฆ-coordinate is five. And we need to place our
ordered pair inside brackets. The ordered pair for the
location of the monkeys is four, five.

Which point is at four,
six?

In this question, we are shown
five different points on our coordinate plane: points ๐ด, ๐ต, ๐ถ, ๐ท, and
๐ธ. And we have to identify the
point which is at four, six. When we see an ordered pair or
a pair of coordinates, we have to remember that the ๐ฅ-coordinate always comes
first followed by the ๐ฆ-coordinate. So, we know that number four is
the ๐ฅ-coordinate. If we start at four on the
๐ฅ-axis and draw a line going up, this will help us to identify which point is
at number four on the ๐ฅ-axis.

So, letโs start drawing from
four on the ๐ฅ-axis. Can you see which point weโre
going to reach? It looks like our point is
point ๐ธ. But we need to check the
๐ฆ-coordinate, which is six. So, letโs find six on the
๐ฆ-axis and draw our line across until we reach a point. Here we go. Hereโs six on the ๐ฆ-axis. And if we join our point along
this line, again we reach point ๐ธ. The point which is at four, six
is point ๐ธ.

What are the coordinates of the
missing point which would complete the square?

In this question, we have to
complete the partially drawn square, and then we have to write the coordinates
of this missing point. Letโs start by thinking about
where to draw the missing point. It would go here, letโs join up
the points to complete the square. There we go. Now, we need to write the
coordinates of this point. When we write a pair of
coordinates, we always write the ๐ฅ-coordinate first.

This orange line is the
๐ฅ-axis. We need to draw a line from our
point down to the ๐ฅ-axis. Now, we can see the
๐ฅ-coordinate is six. Letโs do the same to find the
๐ฆ-coordinate: draw a line from our point all the way along to the ๐ฆ-axis. The pink line shows our
๐ฆ-axis. And by drawing a line from our
point to the ๐ฆ-axis, we can see the ๐ฆ-coordinate is three. The coordinates of the missing
point which would complete the square are six, three. Our ๐ฅ-coordinate is six and
our ๐ฆ-coordinate is three.

What have we learned in this
video? Weโve learned how to find the ๐ฅ-
and ๐ฆ-coordinates of a point in the first quadrant. And we also learned how to locate a
point given its coordinates.