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NCERT Exemplar · Class 9 Mathematics Coordinate Geometry

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EXERCISE 3.1 1–10 (part 1 of 6)

  1. Write the correct answer in each of the following :

    Exercise 1

    Point (−3,5)\displaystyle (-3, 5) lies in the (A) first quadrant (B) second quadrant (C) third quadrant (D) fourth quadrant

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    NCERT’s answer
    (B)
    (B) second quadrant.\[x=-3<0,\quad y=5>0 \]Negative abscissa, positive ordinate — the point sits left of the \(\displaystyle y\)-axis and above the \(\displaystyle x\)-axis.NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-1_Q1

  2. Exercise 2

    Signs of the abscissa and ordinate of a point in the second quadrant are respectively (A) +,+ (B) -, - (C) -, + (D) +, -

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    NCERT’s answer
    (C)
    (C) \(\displaystyle -, +\).Quadrant II lies to the left of the \(\displaystyle y\)-axis and above the \(\displaystyle x\)-axis, so the abscissa is negative and the ordinate positive.

  3. Exercise 3

    Point (0,−7)\displaystyle (0, -7) lies (A) on the x\displaystyle x-axis (B) in the second quadrant (C) on the y\displaystyle y-axis (D) in the fourth quadrant

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    NCERT’s answer
    (C)
    (C) on the \(\displaystyle y\)-axis. \[x = 0 \] A zero abscissa places the point on the \(\displaystyle y\)-axis, whatever its ordinate. NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-1_Q3

  4. Exercise 4

    Point (−10,0)\displaystyle (- 10, 0) lies (A) on the negative direction of the x\displaystyle x-axis (B) on the negative direction of the y\displaystyle y-axis (C) in the third quadrant (D) in the fourth quadrant

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    NCERT’s answer
    (A)
    (A) on the negative direction of the \(\displaystyle x\)-axis. \[y = 0, \quad x = -10 < 0 \] Zero ordinate puts it on the \(\displaystyle x\)-axis; the negative abscissa puts it on that axis's negative side. NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-1_Q4

  5. Exercise 5

    Abscissa of all the points on the x\displaystyle x-axis is (A) 0\displaystyle 0 (B) 1\displaystyle 1 (C) 2\displaystyle 2 (D) any number

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    NCERT’s answer
    (D)
    (D) any number.Every point on the \(\displaystyle x\)-axis has the form \(\displaystyle (x, 0)\) — the ordinate is fixed at \(\displaystyle 0\), but the abscissa \(\displaystyle x\) is unrestricted.

  6. Exercise 6

    Ordinate of all points on the x\displaystyle x-axis is (A) 0\displaystyle 0 (B) 1\displaystyle 1 (C) - 1\displaystyle 1 (D) any number

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    NCERT’s answer
    (A)
    (A) \(\displaystyle 0\).Every point on the \(\displaystyle x\)-axis is \(\displaystyle (x, 0)\): the ordinate is fixed at \(\displaystyle 0\) whatever \(\displaystyle x\) is.

  7. Exercise 7

    The point at which the two coordinate axes meet is called the (A) abscissa (B) ordinate (C) origin (D) quadrant

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    NCERT’s answer
    (C)
    (C) origin.The \(\displaystyle x\)-axis and \(\displaystyle y\)-axis intersect at the single point \(\displaystyle (0,0)\), named the origin.

  8. Exercise 8

    A point both of whose coordinates are negative will lie in (A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant

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    NCERT’s answer
    (C)
    (C) III quadrant.\[x < 0, \quad y < 0 \]Both coordinates negative is exactly the sign pattern of quadrant III.

  9. Exercise 9

    Points (1,−1)\displaystyle (1, - 1), (2,−2)\displaystyle (2, - 2), (4,−5)\displaystyle (4, - 5), (−3,−4)\displaystyle (- 3, - 4) (A) lie in II quadrant (B) lie in III quadrant (C) lie in IV quadrant (D) do not lie in the same quadrant

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    NCERT’s answer
    (D)
    (D) do not lie in the same quadrant. \[A(1,-1),\ B(2,-2),\ C(4,-5):\quad x>0,\ y<0\ \Rightarrow\ \text{IV} \] \[D(-3,-4):\quad x<0,\ y<0\ \Rightarrow\ \text{III} \] Three points sit in quadrant IV, the fourth in quadrant III. NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-1_Q9

  10. Exercise 10

    If y\displaystyle y coordinate of a point is zero, then this point always lies (A) in I quadrant (B) in II quadrant (C) on x\displaystyle x - axis (D) on y\displaystyle y - axis

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    NCERT’s answer
    (C)
    (C) on \(\displaystyle x\)-axis.\[y = 0 \]Every point with zero ordinate lies on the \(\displaystyle x\)-axis, whatever its abscissa.