5 min readConcept sheet1-mark MCQ and assertion-reason; the basics are used in every coordinate question

The coordinate plane (review)

Every point has an address (x, y): x is its distance from the y-axis and y is its distance from the x-axis. The signs tell the quadrant.

Abscissa and ordinateIn P(x, y), x is the abscissa (x-coordinate) and y is the ordinate (y-coordinate)

Signs in the quadrantsI (+, +), II (−, +), III (−, −), IV (+, −)

Points on the axesOn the x-axis: (x, 0). On the y-axis: (0, y). Origin: (0, 0)

Same horizontal linePoints with the same y; distance = difference of the x-coordinates

The coordinate plane

Two number lines cross at right angles at the origin O (0, 0). The horizontal line is the x-axis and the vertical line is the y-axis. They split the plane into four quadrants, numbered I to IV anticlockwise from the top right. A point P is written (x, y). The x-coordinate (abscissa) is its distance from the y-axis. The y-coordinate (ordinate) is its distance from the x-axis. The signs show which side it is on.

Signs and positions

Where the point is	Sign of x	Sign of y	Example
Quadrant I	+	+	(3, 2)
Quadrant II	−	+	(−4, 1)
Quadrant III	−	−	(−2, −5)
Quadrant IV	+	−	(6, −3)
On the x-axis	any	0	(−7, 0)
On the y-axis	0	any	(0, 4)

How to draw the axes and plot a point, e.g. (−3, 2)

1
Draw the x-axis and the y-axis on graph paper and mark O. Choose a scale, e.g. 1 cm = 1 unit, and write it.
2
Number both axes: positive to the right and up, negative to the left and down.
3
Start at O and move 3 units to the left (x = −3).
4
From there move 2 units up (y = 2). Put a dot and write P(−3, 2) beside it.

Example 1: distance along a line

Problem

Find the distance between A(2, 3) and B(9, 3).

Working

Both points have y = 3, so AB is a horizontal line.
On a horizontal line, distance = difference of the x-coordinates.
AB = 9 − 2 = 7 units

Answer

AB = 7 units

Example 2: reading a town map

Problem

A town map is drawn on a grid with the bus stand at the origin. The school is at (4, −3) and the temple is at (−4, −3). In which quadrants are they, and how far apart are they?

Working

School (4, −3): x is positive and y is negative, so it is in quadrant IV.
Temple (−4, −3): both are negative, so it is in quadrant III.
Both have y = −3, so they lie on one horizontal line.
Distance = 4 − (−4) = 8 units

Answer

The school is in quadrant IV and the temple in quadrant III. They are 8 units apart.

In real life

Cinema seats (row and seat number) and squares on a chessboard work like coordinates. So do latitude and longitude on a map of India: two numbers fix one place.

Exam angle

1 marks: “In which quadrant does the point (−2, 7) lie?” Quadrant II, because x is negative and y is positive.

1 marks: “On which axis does the point (0, −5) lie?” On the y-axis, 5 units below the origin, because x = 0.

2 marks: “Find the distance of the point (−6, 8) from the x-axis and from the y-axis.” From the x-axis: the size of y, 8 units. From the y-axis: the size of x, 6 units.

Remember it

Go across, then up or down. Quadrant signs, anticlockwise: (+, +), (−, +), (−, −), (+, −).