CBSE Class 9 Mathematics · Ch 1: Orienting Yourself: The Use of Coordinates

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Difficulty: 3 easy · 7 medium · 20 hard

Sample questions with answers

The first 5 questions of this free test.

1. Q1. The four corners of a rectangular park are marked at $(1, 1)$, $(5, 1)$, $(5, 4)$ and $(1, 4)$, where each unit is $1$ metre. What is the perimeter of the park?

   • A. $12$ metres
   • B. $24$ metres
   • C. $7$ metres
   • D. $14$ metres
   Solution

   The length is $5-1 = 4$ m and the breadth is $4-1 = 3$ m, so the perimeter is $2(4+3) = 14$ m.

2. Q2. Four points are given: $P(3, 0)$, $Q(-5, 0)$, $R(0, 0)$ and $S(0, 7)$. Three of them share one special feature, and one is the "odd one out". Which point is the odd one out?

   • A. $S(0, 7)$
   • B. $Q(-5, 0)$
   • C. $R(0, 0)$
   • D. $P(3, 0)$
   Solution

   $P$, $Q$ and $R$ all have $y$-coordinate $0$ so they lie on the $x$-axis, while $S$ has $x=0$ and lies on the $y$-axis.

3. Q3. Assertion (A): The point $(0, -4)$ lies on the $y$-axis. Reason (R): A point lies on the $y$-axis when its $x$-coordinate is $0$. Choose the correct option.

   • A. A is false, but R is true
   • B. Both A and R are true, but R is not the correct explanation of A
   • C. A is true, but R is false
   • D. Both A and R are true, and R is the correct explanation of A
   Solution

   Both statements are true, and the reason correctly explains why $(0,-4)$ is on the $y$-axis, since its $x$-coordinate is $0$.

4. Q4. Study the following statements: (i) The point $(0, -4)$ lies on the $y$-axis. (ii) The point $(-2, -7)$ lies in the third quadrant. (iii) The coordinates $(3, 5)$ and $(5, 3)$ represent the same point. Which of the statements are correct?

   • A. (i) and (iii) only
   • B. (ii) and (iii) only
   • C. (i) and (ii) only
   • D. (i), (ii) and (iii)
   Solution

   $(0,-4)$ has $x=0$ so it is on the $y$-axis, and $(-2,-7)$ has both coordinates negative so it is in the third quadrant; but $(3,5)$ and $(5,3)$ are different because order matters.

5. Q5. To describe the exact position of a city on the Earth, we state both its latitude and its longitude. Which key idea about coordinates does this real-life example illustrate?

   • A. Only direction, not distance, matters on the Earth
   • B. One number is enough to fix a location on a surface
   • C. Two numbers are needed to fix a unique location on a surface
   • D. Latitude and longitude mean the same thing
   Solution

   Just like $(x, y)$ on a plane, two numbers (latitude and longitude) are needed to fix one unique point on a surface.

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