Mathematics · Textbook solutions

Co-ordinate Geometry

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 42 questions

Practice Set 7.1

6 q
  1. Ex 7.1 Q1
    State in which quadrant or on which axis do the following points lie. A(−3,2)(-3, 2), B(−5,−2)(-5, -2), K(3.5,1.5)(3.5, 1.5), D(2,10)(2, 10), E(37,35)(37, 35), F(15,−18)(15, -18), G(3,−7)(3, -7), H(0,−5)(0, -5), M(12,0)(12, 0), N(0,9)(0, 9), P(0,2.5)(0, 2.5), Q(−7,−3)(-7, -3)
  2. In which quadrant are the following points ?
    Ex 7.1 Q2(i)
    whose both co-ordinates are positive.
  3. Ex 7.1 Q2(ii)
    whose both co-ordinates are negative.
  4. Ex 7.1 Q2(iii)
    whose xx co-ordinate is positive, and the yy co-ordinate is negative.
  5. Ex 7.1 Q2(iv)
    whose xx co-ordinate is negative and yy co-ordinate is positive.
  6. Ex 7.1 Q3
    Draw the co-ordinate system on a plane and plot the following points. L(−2,4)(-2, 4), M(5,6)(5, 6), N(−3,−4)(-3, -4), P(2,−3)(2, -3), Q(6,−5)(6, -5), S(7,0)(7, 0), T(0,−5)(0, -5)

Practice Set 7.2

14 q
  1. Ex 7.2 Q1
    On a graph paper plot the points A(3,0)(3,0), B(3,3)(3,3), C(0,3)(0,3). Join A, B and B, C. What is the figure formed ?
  2. Ex 7.2 Q2
    Write the equation of the line parallel to the Y-axis at a distance of 7 units from it to its left.
  3. Ex 7.2 Q3
    Write the equation of the line parallel to the X-axis at a distance of 5 units from it and below the X-axis.
  4. Ex 7.2 Q4
    The point Q(−3,−2)(-3, -2) lies on a line parallel to the Y-axis. Write the equation of the line and draw its graph.
  5. Ex 7.2 Q5
    X-axis and line x=−4x = -4 are parallel lines. What is the distance between them ?
  6. Which of the equations given below have graphs parallel to the X-axis, and which ones have graphs parallel to the Y-axis ?
    Ex 7.2 Q6(i)
    x=3x = 3
  7. Ex 7.2 Q6(ii)
    y−2=0y - 2 = 0
  8. Ex 7.2 Q6(iii)
    x+6=0x + 6 = 0
  9. Ex 7.2 Q6(iv)
    y=−5y = -5
  10. Ex 7.2 Q7
    On a graph paper, plot the points A(2,3)(2, 3), B(6,−1)(6, -1) and C(0,5)(0, 5). If those points are collinear then draw the line which includes them. Write the co-ordinates of the points at which the line intersects the X-axis and the Y-axis.
  11. Ex 7.2 Q8
    Draw the graphs of the following equations on the same system of co-ordinates. Write the co-ordinates of their points of intersection. x+4=0x + 4 = 0, y−1=0y - 1 = 0, 2x+3=02x + 3 = 0, 3y−15=03y - 15 = 0
  12. Draw the graphs of the equations given below.
    Ex 7.2 Q9(i)
    x+y=2x + y = 2
  13. Ex 7.2 Q9(ii)
    3x−y=03x - y = 0
  14. Ex 7.2 Q9(iii)
    2x+y=12x + y = 1

Problem Set 7

22 q
  1. Choose the correct alternative answer for the following questions.
    Prob Q1(i)
    What is the form of co-ordinates of a point on the X-axis ?
    1. A.
      (b,b)(b, b)
    2. B.
      (0,b)(0, b)
    3. C.
      (a,0)(a, 0)
    4. D.
      (a,a)(a, a)
  2. Prob Q1(ii)
    Any point on the line y=xy = x is of the form .....
    1. A.
      (a,a)(a, a)
    2. B.
      (0,a)(0, a)
    3. C.
      (a,0)(a, 0)
    4. D.
      (a,−a)(a, -a)
  3. Prob Q1(iii)
    What is the equation of the X-axis ?
    1. A.
      x=0x = 0
    2. B.
      y=0y = 0
    3. C.
      x+y=0x + y = 0
    4. D.
      x=yx = y
  4. Prob Q1(iv)
    In which quadrant does the point (−4,−3)(-4, -3) lie ?
    1. A.
      First
    2. B.
      Second
    3. C.
      Third
    4. D.
      Fourth
  5. Prob Q1(v)
    What is the nature of the line which includes the points (−5,5)(-5,5), (6,5)(6,5), (−3,5)(-3,5), (0,5)(0,5) ?
    1. A.
      Passes through the origin
    2. B.
      Parallel to Y-axis
    3. C.
      Parallel to X-axis
    4. D.
      None of these
  6. Prob Q1(vi)
    Which of the points P(−1,1)(-1,1), Q(3,−4)(3,-4), R(1,−1)(1,-1), S(−2,−3)(-2,-3), T(−4,4)(-4,4) lie in the fourth quadrant ?
    1. A.
      P and T
    2. B.
      Q and R
    3. C.
      only S
    4. D.
      P and R
  7. Some points are shown in the figure 7.11. With the help of it answer the following questions :
    Prob Q2(i)
    Write the co-ordinates of the points Q and R.
  8. Prob Q2(ii)
    Write the co-ordinates of the points T and M.
  9. Prob Q2(iii)
    Which point lies in the third quadrant ?
  10. Prob Q2(iv)
    Which are the points whose xx and yy co-ordinates are equal ?
  11. Without plotting the points on a graph, state in which quadrant or on which axis do the following points lie.
    Prob Q3(i)
    (5,−3)(5, -3)
  12. Prob Q3(ii)
    (−7,−12)(-7, -12)
  13. Prob Q3(iii)
    (−23,4)(-23, 4)
  14. Prob Q3(iv)
    (−9,5)(-9, 5)
  15. Prob Q3(v)
    (0,−3)(0, -3)
  16. Prob Q3(vi)
    (−6,0)(-6, 0)
  17. Prob Q4
    Plot the following points on the one and the same co-ordinate system. A(1,3)(1, 3), B(−3,−1)(-3, -1), C(1,−4)(1, -4), D(−2,3)(-2, 3), E(0,−8)(0, -8), F(1,0)(1, 0)
  18. In the graph alongside, line LM is parallel to the Y-axis. (Fig. 7.12)
    Prob Q5(i)
    What is the distance of line LM from the Y-axis ?
  19. Prob Q5(ii)
    Write the co-ordinates of the points P, Q and R.
  20. Prob Q5(iii)
    What is the difference between the xx co-ordinates of the points L and M ?
  21. Prob Q6
    How many lines are there which are parallel to X-axis and having a distance 5 units ?
  22. Prob Q7
    If 'aa' is a real number, what is the distance between the Y-axis and the line x=ax = a ?