Class 9 Maths

Coordinate Geometry

Exercise 3.2

Question 1: Write the answer of each of the following questions:

(a) What is the name of the horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

Answer: x-axis and y-axis

(b) What is the name of each part of the plane formed by these two lines?

Answer: Quadrant

(c) Write the name of the point where these two lines intersect.

Answer: Origin

Question 2: See the given figure and write the following:

coordinates of points
  1. The coordinates of B
  2. The coordinates of C
  3. The point identified by the coordinates (-3, -5)
  4. The point identified by the coordinates (2, -4)
  5. The abscissa of the point D.
  6. The ordinate of the point H.
  7. The coordinates of the point L.
  8. The coordinates of the point M.

Answer: (a) (-5, 2), (b) (5,-5), (c) E, (d) G, (e) 6, (f) -3, (g) (0, 5), (h) (-3, 0)

Exercise 3.3

Question 1: In which quadrant or on which axis do each of the points (-2, 4), (3, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane.

Answer: (-2, 4) quadrant II, (3, -1) quadrant IV, (-1,0) on x-axis and (-3, -5) quadrant III

Question 2: Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

x-2-1 013
y87 -1.253-1

Answer:

coordinates of points

Number System

Numbers are in the form of p/q or can be written in the form of p/q are called rational numbers.

Polynomials

Algebraic expression with many terms having variables and coefficients is called polynomial.

Coordinate Geometry

The distance of a point from the y - axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate.

Linear Equations in Two Variables

A linear equation in two variables has infinite number of solutions.

Euclid's Geometry

The basic concept about a line is that it should be straight and that it should extend indefinitely in both the directions.

Lines & Angles

An angle is formed by two rays originating from the same end point. The rays making an angle are called the arms of the angle and the end-points are called the vertex of the angle.

Triangles

Two figures are congruent, if they are of the same shape and of the same size. Two circles of the same radii are congruent. Two squares of the same sides are congruent.

Quadrilaterals

Sum of the angles of a quadrilateral is 360°. A diagonal of a parallelogram divides it into two congruent triangles.

Parallelograms

In a parallelogram: opposite sides are equal, opposite angles are equal, and diagonals bisect each other

Circles

The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.

Heron's Formula

Heron's formula is generally used for calculating area of scalene triangle.

Surface Area

How to calculate surface area of cylinder, cone and sphere?

Volume

How to calculate volume of cylinder, cone and sphere?

Statistics

Learn to make bar chart and histogram from given data.

Probability

Probability tells about likelihood of an event to occur.