Coordinate Geometry

As (–7, 0) ^{_{$\leftrightarrow $}} (x, y), where x coordinate is -7, i.e. negative and y coordinate is 0, so the point (–7, 0) lies on the negative x-axis.

In the Cartesian plane, the x-axis is the horizontal axis.

Point (- 5, 0) corresponds to (x, y).
Here, x-coordinate is - 5, i.e. negative and y-coordinate is 0.
$\Rightarrow$So, the point (- 5, 0) lies on the negative x-axis.

The vertical (standing) axis of a Cartesian plane is y-axis.

The horizontal and vertical axis drawn on the plane divides the whole plane into quadrants.

(–5, –4) $\Rightarrow$ Both x and y coordinates are negative.
When x < 0 and y < 0, the point lies in the third quadrant.
So, the point (–5, –4) lies in the third quadrant. 

As the point $\biggl(- \frac{2}{3}, 0\biggr) \leftrightarrow (x,y) $
Here, x co-ordinate is $\frac{-2}{3}$, which is negative and y co-ordinate is 0.
So, the point $\biggl(- \frac{2}{3}, 0\biggr)$lies on the negative x-axis.

The meeting point of two axes in the Cartesian plane is called origin (0, 0).

The point is $\biggl(\frac{4}{5}, -2 \biggr)$.
It corresponds to (x, y).
When x > 0 and y < 0, the point lies in the 4^th quadrant.
So, the point $\biggl( \frac{4}{5}, -2 \biggr)$ lies in the 4^th quadrant.

The point is (0, – 11) ^{_{$\leftrightarrow $}} (x, y)
Here, x-coordinate is 0 and y-coordinate is – 11.
So, the point lies on the negative y-axis.

The perpendicular distance of the point (6, – 5) from the x-axis will be y-coordinate but with a positive sign as distance is never negative.
So, the perpendicular distance of (6, – 5) from the x-axis is 5 units.

The point (0, 3) ^{_{$\leftrightarrow $}} (x, y)
Here, the x-coordinate is 0 and the y-coordinate is 3.
$\therefore$ The point (0, 3) lies on the positive y-axis.

The y co-ordinate is also known as ordinate and b is the y co-ordinate of point (a, b).
So, 'b' is called ordinate.

The point is (17, 9) $\leftrightarrow $ (x, y)
Here, x > 0 and y > 0 and if x is positive and y is positive, then the point lies in the 1^st quadrant.
So, point (17, 9) lies in the first quadrant.
                                                OR
The sign of co-ordinate of a point is (+, +), which lies in 1^st quadrant.
So, (17, 9) lies in the first quadrant.

As the point is (8, 0)
        (8, 0) $\leftrightarrow $ (x, y)
Here, x-coordinate is 8 which is greater than 0 and y-coordinate is 0, and when y-coordinate is 0, then the point lies on x–axis.
As the x-coordinate is greater than 0, the point (8, 0) lies on positive x–axis.

The perpendicular distance from y<span style="font-family:" arial;="" font-size:="" small;="">–axis of any point is x co-ordinate but distance is always positive.
So, the perpendicular distance of (– 7, 9) from y<span style="font-family:" arial;="" font-size:="" small;="">–axis is 7 units.

The point is (11, – 15).
Here, x-coordinate is 11 > 0 and y-coordinate is – 15 < 0, and the signs of the coordinates are (+, –),
which lie in the 4^th quadrant.
So, the point (11, – 15) lies in the 4^th quadrant.

When x-coordinate is 0, the point lies on the y–axis.
$\therefore$ The point (0, 6) lies on the positive y–axis.

The perpendicular distance from y<span style="font-family:" arial;="" font-size:="" small;="">–axis of any point is x co-ordinate but distance can never be negative.
So, the perpendicular distance of (13, 12) from y<span style="font-family:" arial;="" font-size:="" small;="">–axis is 13.

The point is (– 7, 6).
Here, x co-ordinate is – 7 < 0 and y co-ordinate is 6 > 0
i.e. x < 0 and y > 0, and when x is negative and y is positive, then the point lies in 2^nd quadrant.
So, the point (– 7, 6) lies in the 2^nd quadrant.

As the point is (7, 0),
        (7, 0) $\leftrightarrow $ (x, y)
Here, x co-ordinate is 7 which is positive and y co-ordinate is 0,
and when y co-ordinate is 0, then the point lies on x<span style="font-family:" arial;="" font-size:="" small;="">–axis.
So, the point (7, 0) lies on positive x<span style="font-family:" arial;="" font-size:="" small;="">–axis.

The point is $\biggl( \frac{-8}{6}, \frac{-7}{3} \biggr)$.
Here, x-coordinate is $\frac{-8}{6}$, which is negative, and y-coordinate is $\frac{-7}{3}$, which is also negative.
i.e. x < 0 and y < 0
When x < 0 and y < 0, the point lies in the third quadrant.
So, the point $\biggl( \frac{-8}{6}, \frac{-7}{3} \biggr)$ lies in the third quadrant.

The perpendicular distance of a point (- 2, - 4) from x-axis will be y co-ordinate but with a positive sign, as the distance is never negative.
So, the perpendicular distance of (- 2, - 4) from x-axis is 4 units.

The point is (0, – 3).
Here, y co-ordinate is – 3, which is negative
and when x co-ordinate is zero, then the point lies on y-axis.
So, the point (0, – 3) lies on the negative y-axis.

The point is (– 2, 5).
Here, x-co-ordinate is – 2 < 0 and y co-ordinate is 5 > 0.
And when x < 0 and y > 0 in the point (x, y), then the point lies in the second quadrant.
So, the point (– 2, 5) lies in the 2^nd quadrant.
                                                            OR
The signs of the co-ordinates of point are (–, +), which lies in the 2^nd quadrant.
So, the point (– 2, 5) lies in the 2^nd quadrant.

The perpendicular distance of the point (11, –9) from the x-axis will be y coordinate of the point, but with a positive sign as the distance is never negative.
So, the perpendicular distance of (11, –9) from the x-axis is 9 units.

The point is (7, 3) $\leftrightarrow $ (x, y)
Here, x > 0 and y > 0,
and when x > 0 and y > 0, the point (x, y) lies in the first quadrant.
Then, the point (7, 3) lies in the 1^st quadrant.

As the point is (6, 0),
            (6, 0) $\leftrightarrow $ (x, y)
Here, x co-ordinate is 6, which is positive and y co-ordinate is 0.
When y co-ordinate of a point is 0, then the point lies on x-axis.
So, the point (6, 0) lies on positive x-axis.

The point is (4, – 8).
Here, x co-ordinate is 4 > 0 and y co-ordinate is – 8 < 0.
When x > 0 and y < 0, then the point (x, y) lies in the 4^th quadrant.
So, the point (4, – 8) lies in the fourth quadrant.
                                                OR
The signs of co-ordinates of point are (+, –), which lies in the 4^th quadrant.
So, the point (4, – 8) lies in the 4^th quadrant.

The point is (– 7, – 9).
Here, x co-ordinate is – 7, which is negative
and y co-ordinate is – 9, which is also negative.
When x < 0 and y < 0, then the point (x, y) lies in the third quadrant.
So, the point (– 7, – 9) lies in the third quadrant.
                                                OR
The signs of co-ordinates of the point are (–, –), which lies in the 3^rd quadrant.
So, the point <span style="font-family:" arial;="" font-size:="" small;="">(– 7, – 9) lies in the third quadrant.

Since ordered pair is written in the order (x, y), where x = x coordinate of that point and y = y coordinate of that point, so the ordered pair for point D is (11, –6). 

Because ordered pair representing any point is written as (x, y), where x = x-coordinate of that point and y = y-coordinate of that point.
^{_$\therefore$}    The ordered pair representing the point E is (11, 3).

The point B lies on y-axis; so the x-coordinate must be zero and y-coordinate must be 3.
Thus, the ordered pair representing the point B is (0, 3).

 (–8, 7) represents point A on the graph.

The ordered pair representing C is (– 10, – 8) as the ordered pairs are written in the order (x, y),
where x = x-coordinate of the point and y = y-coordinate of the point.

The ordered pair representing point H is (5, – 12) as ordered pairs are written in the order (x, y),
where x = x-coordinate of the point and y = y-coordinate of the point.

As the ordered pair representing a point is written as (x, y), where x = x-coordinate of the point and y = y-coordinate of the point.
Then, the ordered pair representing I is (3, 13).

As the ordered pair for any point is written in the form (x, y), where x = x co-ordinate of the point and y = y co-ordinate of the point.
Then, the ordered pair representing F is given by (- 6, 10).

As the ordered pair representing any point is given by (x, y), where x = x co-ordinate of the point and y = y co-ordinate of the point.
Then, the ordered pair representing J is given by (6, 6).

As the ordered pair representing any point is given by (x, y), where x = x co-ordinate of that point and y = y co-ordinate of that point.
Then, the ordered pair representing G is given by (- 5, - 10).