SolveItNCERT · CBSE Boards

NCERT Exemplar · Class 9 Mathematics Coordinate Geometry

42 questions · 42 still being checked

EXERCISE 3.3 1–12 (part 5 of 6)

  1. Exercise 1

    Write the coordinates of each of the points P,Q,R,S,T\displaystyle \mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}, \mathrm{T} and O from the Fig. 3.5. NCERT_Question_Class9_Maths_Exemplar_Ch3_Ex3-3_Q1

    Check this one against your book

    NCERT’s printed answer for this exercise does not match its own question. This working follows the question as printed.

    NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q1 \[P = (1, 1), \quad S = (2, 1), \quad Q = (-3, 0) \] \[R = (-2, -3), \quad T = (4, -2), \quad O = (0, 0) \] Answer: P$\displaystyle (1, 1)$, Q$\displaystyle (-3, 0)$, R$\displaystyle (-2, -3)$, S$\displaystyle (2, 1)$, T$\displaystyle (4, -2)$, O$\displaystyle (0, 0)$.NCERT prints: R\(\displaystyle (-3,-2)\) — the figure's own dot for R sits under the \(\displaystyle x=-2\) tick, level with \(\displaystyle y=-3\), so the printed pair is transposed.

  2. Exercise 2

    Plot the following points and write the name of the figure obtained by joining them in order: P(−3,2),Q(−7,−3),R(6,−3),S(2,2)\displaystyle \mathrm{P}(-3,2), \mathrm{Q}(-7,-3), \mathrm{R}(6,-3), \mathrm{S}(2,2)

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    Trapezium
    \[P(-3, 2), \quad Q(-7, -3), \quad R(6, -3), \quad S(2, 2) \] NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q2 \[Q, R \text{ and } S, P \text{ share an ordinate} \ \Rightarrow\ QR \parallel SP \text{ (both horizontal)} \] \[QR = 6-(-7) = 13, \qquad SP = 2-(-3) = 5 \] One pair of sides parallel, the pair unequal in length. Answer: PQRS is a trapezium.

  3. Exercise 3

    Plot the points (x,y)\displaystyle (x, y) given by the following table:
    x\displaystyle x2\displaystyle 24\displaystyle 4-3\displaystyle 3-2\displaystyle 23\displaystyle 30\displaystyle 0
    y\displaystyle y4\displaystyle 42\displaystyle 20\displaystyle 05\displaystyle 5-3\displaystyle 30\displaystyle 0

    Not cross-checked

    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    Reading the table column-wise gives six points: \[(2, 4), \quad (4, 2), \quad (-3, 0), \quad (-2, 5), \quad (3, -3), \quad (0, 0) \] NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q3 Answer: the six points are plotted as shown; \(\displaystyle (0,0)\) is the origin \(\displaystyle O\).

  4. Exercise 4

    Plot the following points and check whether they are collinear or not : (i) (1,3)\displaystyle (1, 3), (−1,−1)\displaystyle (- 1, - 1), (−2,−3)\displaystyle (- 2, - 3) (ii) (1,1)\displaystyle (1, 1), (2,−3)\displaystyle (2, - 3), (−1,−2)\displaystyle (- 1, -2) (iii) (0,0)\displaystyle (0, 0), (2,2)\displaystyle (2, 2), (5,5)\displaystyle (5, 5)

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (i)
    Collinear (ii) Not collinear (iii) Collinear
    \[\text{(i)}\ A(1,3),\ B(-1,-1),\ C(-2,-3) \] \[y = 2x+1 \quad \text{(the line through A and B)} \] \[C:\ 2(-2)+1 = -3 = y_C \quad \Rightarrow\ \text{collinear} \] \[\text{(ii)}\ A(1,1),\ B(2,-3),\ C(-1,-2) \] \[y = -4x+5 \quad \text{(the line through A and B)} \] \[C:\ -4(-1)+5 = 9 \ne -2 = y_C \quad \Rightarrow\ \text{not collinear} \] \[\text{(iii)}\ A(0,0),\ B(2,2),\ C(5,5) \] \[y = x \quad \text{(the line through A and B)} \] \[C:\ 5 = 5 \quad \Rightarrow\ \text{collinear} \] NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q4 Answer: (i) collinear (ii) not collinear (iii) collinear.

  5. Exercise 5

    Without plotting the points indicate the quadrant in which they will lie, if (i) ordinate is 5\displaystyle 5 and abscissa is - 3\displaystyle 3 (ii) abscissa is - 5\displaystyle 5 and ordinate is - 3\displaystyle 3 (iii) abscissa is - 5\displaystyle 5 and ordinate is 3\displaystyle 3 (iv) ordinate is 5\displaystyle 5 and abscissa is 3\displaystyle 3

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (i)
    II (ii) III (iii) II (iv) I
    \[\text{(i) } (x,y) = (-3, 5):\ x<0,\ y>0 \Rightarrow \text{Quadrant II} \] \[\text{(ii) } (x,y) = (-5, -3):\ x<0,\ y<0 \Rightarrow \text{Quadrant III} \] \[\text{(iii) } (x,y) = (-5, 3):\ x<0,\ y>0 \Rightarrow \text{Quadrant II} \] \[\text{(iv) } (x,y) = (3, 5):\ x>0,\ y>0 \Rightarrow \text{Quadrant I} \] Answer: (i) II (ii) III (iii) II (iv) I.

  6. Exercise 6

    In Fig. 3.6\displaystyle 3.6, LM is a line parallel to the y\displaystyle y-axis at a distance of 3\displaystyle 3 units. (i) What are the coordinates of the points P, R and Q? (ii) What is the difference between the abscissa of the points L and M? NCERT_Question_Class9_Maths_Exemplar_Ch3_Ex3-3_Q6

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (i)
    P$\displaystyle (3, 2)$, R$\displaystyle (3, 0)$, Q$\displaystyle (3, -1)$ (ii) $\displaystyle 0$
    NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q6 \[L = (3, 4), \quad P = (3, 2), \quad R = (3, 0), \quad Q = (3, -1), \quad M = (3, -3) \] \[\text{abscissa of } L - \text{abscissa of } M = 3 - 3 = 0 \] Answer: P$\displaystyle (3, 2)$, R$\displaystyle (3, 0)$, Q$\displaystyle (3, -1)$; difference of abscissas \(\displaystyle = 0\).

  7. Exercise 7

    In which quadrant or on which axis each of the following points lie? (−3,5)\displaystyle (-3, 5), (4,−1)\displaystyle (4, -1), (2,0)\displaystyle (2, 0), (2,2)\displaystyle (2, 2), (−3,−6)\displaystyle (- 3, -6)

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    II, IV, $\displaystyle x$-axis, I, III
    NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q7 \[(-3, 5):\ x<0,\ y>0 \Rightarrow \text{Quadrant II} \] \[(4, -1):\ x>0,\ y<0 \Rightarrow \text{Quadrant IV} \] \[(2, 0):\ y = 0 \Rightarrow \text{on the } x\text{-axis} \] \[(2, 2):\ x>0,\ y>0 \Rightarrow \text{Quadrant I} \] \[(-3, -6):\ x<0,\ y<0 \Rightarrow \text{Quadrant III} \] Answer: II, IV, x-axis, I, III (in that order).

  8. Exercise 8

    Which of the following points lie on y\displaystyle y-axis? A (1,1)\displaystyle (1, 1), B (1,0)\displaystyle (1, 0), C (0,1)\displaystyle (0, 1), D (0,0)\displaystyle (0, 0), E (0,−1)\displaystyle (0, - 1), F (−1,0)\displaystyle (- 1, 0), G (0,5)\displaystyle (0, 5), H (−7,0)\displaystyle (- 7, 0), I (3,3)\displaystyle (3, 3).

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    C, D, E, G
    NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q8 \[\text{a point lies on the } y\text{-axis} \iff \text{abscissa} = 0 \] \[C(0, 1), \quad D(0, 0), \quad E(0, -1), \quad G(0, 5) \] Answer: C, D, E, G.

  9. Exercise 9

    Plot the points (x,y)\displaystyle (x, y) given by the following table. Use scale 1 cm=0.25\displaystyle 1 \mathrm{~cm}=0.25 units
    x\displaystyle x1.25\displaystyle 1.250.25\displaystyle 0.251.5\displaystyle 1.5-1.75\displaystyle 1.75
    y\displaystyle y-0.5\displaystyle 0.51\displaystyle 11.5\displaystyle 1.5-0.25\displaystyle 0.25

    Not cross-checked

    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    Reading the table column-wise gives four points, to be plotted at the scale \(\displaystyle 1\text{ cm} = 0.25\) units: \[1:(1.25,-0.5),\ \ 2:(0.25,1),\ \ 3:(1.5,1.5),\ \ 4:(-1.75,-0.25) \] NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q9 Answer: the four points, plotted as shown — two in quadrant I, one in quadrant III, one in quadrant IV.

  10. Exercise 10

    A point lies on the x\displaystyle x-axis at a distance of 7\displaystyle 7 units from the y\displaystyle y-axis. What are its coordinates? What will be the coordinates if it lies on y\displaystyle y-axis at a distance of -7\displaystyle 7 units from x\displaystyle x-axis?

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    $\displaystyle (7, 0)$, $\displaystyle (0, -7)$
    A point on the \(\displaystyle x\)-axis has the form \(\displaystyle (x, 0)\); a distance of \(\displaystyle 7\) units from the \(\displaystyle y\)-axis gives \[x = 7 \quad\Rightarrow\quad (7, 0) \] A point on the \(\displaystyle y\)-axis has the form \(\displaystyle (0, y)\); a distance of \(\displaystyle -7\) units from the \(\displaystyle x\)-axis gives \[y = -7 \quad\Rightarrow\quad (0, -7) \] NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q10 Answer: \(\displaystyle (7, 0)\); \(\displaystyle (0, -7)\).

  11. Exercise 11

    Find the coordinates of the point (i) which lies on x\displaystyle x and y\displaystyle y axes both. (ii) whose ordinate is - 4\displaystyle 4 and which lies on y\displaystyle y-axis. (iii) whose abscissa is 5\displaystyle 5 and which lies on x\displaystyle x-axis.

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    (i)
    $\displaystyle (0,0)$ (ii) $\displaystyle (0,-4)$ (iii) $\displaystyle (5,0)$
    (i)
    The point common to both axes is where they meet:
    \[(0,0) \] (ii) On the \(\displaystyle y\)-axis, \(\displaystyle x=0\); with ordinate \(\displaystyle -4\):
    \[(0,-4) \] (iii) On the \(\displaystyle x\)-axis, \(\displaystyle y=0\); with abscissa \(\displaystyle 5\):
    \[(5,0) \] NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q11
    Answer: (i) \(\displaystyle (0,0)\) (ii) \(\displaystyle (0,-4)\) (iii) \(\displaystyle (5,0)\).

  12. Exercise 12

    Taking 0.5\displaystyle 0.5 cm as 1\displaystyle 1 unit, plot the following points on the graph paper : A(1,3),B(−3,−1),C(1,−4),D(−2,3),E(0,−8),F(1,0)\mathrm{A}(1,3), \mathrm{B}(-3,-1), \mathrm{C}(1,-4), \mathrm{D}(-2,3), \mathrm{E}(0,-8), \mathrm{F}(1,0)

    Not cross-checked

    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    Six points, plotted at the scale \(\displaystyle 0.5\text{ cm} = 1\) unit: \[A(1,3),\ B(-3,-1),\ C(1,-4),\ D(-2,3),\ E(0,-8),\ F(1,0) \] NCERT_Solution_Class9_Maths_Exemplar_Ch3_Ex3-3_Q12 A and D lie in quadrants I and II respectively; B and C lie in quadrants III and IV respectively; E lies on the negative \(\displaystyle y\)-axis, F on the positive \(\displaystyle x\)-axis. Answer: A$\displaystyle (1,3)$ — I; D$\displaystyle (-2,3)$ — II; B$\displaystyle (-3,-1)$ — III; C$\displaystyle (1,-4)$ — IV; E$\displaystyle (0,-8)$ — negative \(\displaystyle y\)-axis; F$\displaystyle (1,0)$ — positive \(\displaystyle x\)-axis.