Coordinate Geometry
ICSE Class 9 · Mathematics · Chapter 23
What this chapter covers
- What coordinate geometry does
- Dependent and independent variables
- Table of values of a relation
- The Cartesian system
- Ordered pairs
- Coordinates of a point
- Quadrants and signs of coordinates
- Plotting points in the Cartesian plane
- Lines parallel to the axes
- Graph of a relation from a table of values
Key points
- An independent variable is chosen freely; a dependent variable is decided by it. In y = f(x) form, x is independent and y is dependent.
- A table of values lists chosen values of x with the matching values of y; each column is an ordered pair (x, y).
- An ordered pair (a, b) depends on order; (a, b) = (c, d) means a = c and b = d.
- The Cartesian system uses two perpendicular number lines, the x-axis and the y-axis, meeting at the origin O(0, 0).
- The abscissa (x) is the directed distance from the y-axis; the ordinate (y) is the directed distance from the x-axis.
- Quadrant signs, anticlockwise from the first: (+, +), (-, +), (-, -), (+, -).
- A point on the x-axis is (a, 0); a point on the y-axis is (0, b); points on the axes lie in no quadrant.
- To plot (a, b): move a units along the x-axis, then b units parallel to the y-axis, using a stated scale.
- y = b is a line parallel to the x-axis; x = a is a line parallel to the y-axis; the axes are y = 0 and x = 0.
- The graph of a linear relation y = mx + c is a straight line; plot at least three points from a table of values and join them.
Questions answered
Define a dependent variable and an independent variable. In the relation C = 25n + 100, which is which?
An independent variable can be given any value freely; a dependent variable takes the value decided by the independent variable. In C = 25n + 100, n is independent and C is dependent.
The cost of sending a parcel is ₹50 plus ₹20 for every kilogram. Write the cost y in terms of the mass x kg, and find the cost of a 7 kg parcel.
y = 20x + 50. For x = 7, y = 140 + 50 = 190, so the cost is ₹190.
Prepare a table of values of y = 2 - 3x for x = -2, -1, 0, 1, 2.
The values of y are 8, 5, 2, -1, -4 respectively.
Find x and y if (3x - 1, y + 4) = (8, 1).
3x - 1 = 8 gives x = 3; y + 4 = 1 gives y = -3.
Why is (4, 7) not the same as (7, 4), although \4, 7\ = \7, 4\?
An ordered pair depends on the order of its components, so the two pairs have different first components and name different points; a set ignores order.
Write the abscissa and ordinate of (-5, 9). How far is the point from each axis?
Abscissa -5, ordinate 9. It is 9 units from the x-axis and 5 units from the y-axis.
In which quadrant or on which axis does each point lie: (-4, -1), (6, -6), (0, 7), (-2, 3), (-8, 0)?
Third quadrant; fourth quadrant; y-axis; second quadrant; x-axis.
Write the coordinates of a point (i) on the x-axis 6 units to the left of the origin, (ii) on the y-axis 2 units below the origin.
(i) (-6, 0) (ii) (0, -2).