Introduction to Coordinate Geometry

 Page 1


Q u e s t i o n : 1
Write the abscissa of each of the following points:
(i)     (0, 5)
(ii)    (3, 7)
(iii)   (–2, 4)
(iv)   (6, –3)
S o l u t i o n :
(i) Abscissa of (0,5) = 0
(ii) Abscissa of (3,7) =3
(iii) Abscissa of (-2,4) = -2
(iv) Abscissa of (6,-3) = 6
Q u e s t i o n : 2
Write the ordinate of each of the following points:
(i)     (4, 0)
(ii)    (5, 2)
(iii)   (1, –4)
(iv)    (–10, –7)
S o l u t i o n :
(i) Ordinate of (4,0) = 0
(ii) Ordinate of (5,2) =2
(iii) Ordinate of (1,-4) =- 4
(iv) Ordinate of (-10,-7) = -7
Q u e s t i o n : 3
On a graph paper, plot each of the following points:
(i)      A (4, 3)
(ii)     B (–2, 5)
(iii)    C (0, 4)
(iv)    D (7, 0)
(v)     E (–3, –5)
(vi)    F (5, –3)
(vii)   G (–5, –5)
(viii)  H (0, 0)
S o l u t i o n :
Page 2


Q u e s t i o n : 1
Write the abscissa of each of the following points:
(i)     (0, 5)
(ii)    (3, 7)
(iii)   (–2, 4)
(iv)   (6, –3)
S o l u t i o n :
(i) Abscissa of (0,5) = 0
(ii) Abscissa of (3,7) =3
(iii) Abscissa of (-2,4) = -2
(iv) Abscissa of (6,-3) = 6
Q u e s t i o n : 2
Write the ordinate of each of the following points:
(i)     (4, 0)
(ii)    (5, 2)
(iii)   (1, –4)
(iv)    (–10, –7)
S o l u t i o n :
(i) Ordinate of (4,0) = 0
(ii) Ordinate of (5,2) =2
(iii) Ordinate of (1,-4) =- 4
(iv) Ordinate of (-10,-7) = -7
Q u e s t i o n : 3
On a graph paper, plot each of the following points:
(i)      A (4, 3)
(ii)     B (–2, 5)
(iii)    C (0, 4)
(iv)    D (7, 0)
(v)     E (–3, –5)
(vi)    F (5, –3)
(vii)   G (–5, –5)
(viii)  H (0, 0)
S o l u t i o n :
Q u e s t i o n : 4
Plot each of the following points on a graph sheet. Verify that they lie on a line.
(i)      A (4, 0),  B (4, 2), C (4, 2.5), and D (4, 6)
(ii)     P (1, 1),  Q (2, 2), R (3, 3), and S (4,4)
(iii)    L (6, 2),  M (5, 3), N (3, 5), and O (2, 6)
S o l u t i o n :
(i) After joining points A, B, C, D, we can see that the given points forms a straight line
(ii) After joining points P, Q ,R, S, we can see that the given points forms a straight line
Page 3


Q u e s t i o n : 1
Write the abscissa of each of the following points:
(i)     (0, 5)
(ii)    (3, 7)
(iii)   (–2, 4)
(iv)   (6, –3)
S o l u t i o n :
(i) Abscissa of (0,5) = 0
(ii) Abscissa of (3,7) =3
(iii) Abscissa of (-2,4) = -2
(iv) Abscissa of (6,-3) = 6
Q u e s t i o n : 2
Write the ordinate of each of the following points:
(i)     (4, 0)
(ii)    (5, 2)
(iii)   (1, –4)
(iv)    (–10, –7)
S o l u t i o n :
(i) Ordinate of (4,0) = 0
(ii) Ordinate of (5,2) =2
(iii) Ordinate of (1,-4) =- 4
(iv) Ordinate of (-10,-7) = -7
Q u e s t i o n : 3
On a graph paper, plot each of the following points:
(i)      A (4, 3)
(ii)     B (–2, 5)
(iii)    C (0, 4)
(iv)    D (7, 0)
(v)     E (–3, –5)
(vi)    F (5, –3)
(vii)   G (–5, –5)
(viii)  H (0, 0)
S o l u t i o n :
Q u e s t i o n : 4
Plot each of the following points on a graph sheet. Verify that they lie on a line.
(i)      A (4, 0),  B (4, 2), C (4, 2.5), and D (4, 6)
(ii)     P (1, 1),  Q (2, 2), R (3, 3), and S (4,4)
(iii)    L (6, 2),  M (5, 3), N (3, 5), and O (2, 6)
S o l u t i o n :
(i) After joining points A, B, C, D, we can see that the given points forms a straight line
(ii) After joining points P, Q ,R, S, we can see that the given points forms a straight line
(iii) After joining points L, M, N, O,  we can see that the given points forms a straight line
Q u e s t i o n : 5
Plot the given points on a graph sheet and check if they lie on a straight line. If not, name the shape they form
when joined in the given order.
(i)      A (0, 2),  B (0, 3.5), C (0, 5) and D (0, 6)
(ii)     P (1, 3),  Q (1, 5), R (3, 3) and S (3, 5)
(iii)    E (4, 5),  F (5, 5), G (5, 7) and H (6, 5)
(iv)    L (2, 0),  M (2, 3), N (0, 3) and O (0, 0)
(v)     J (4, 3),  K (6, 1), L (6, 5) and M (4, 7)
S o l u t i o n :
(i) After joining the given points, we see that they form a straight line.
Page 4


Q u e s t i o n : 1
Write the abscissa of each of the following points:
(i)     (0, 5)
(ii)    (3, 7)
(iii)   (–2, 4)
(iv)   (6, –3)
S o l u t i o n :
(i) Abscissa of (0,5) = 0
(ii) Abscissa of (3,7) =3
(iii) Abscissa of (-2,4) = -2
(iv) Abscissa of (6,-3) = 6
Q u e s t i o n : 2
Write the ordinate of each of the following points:
(i)     (4, 0)
(ii)    (5, 2)
(iii)   (1, –4)
(iv)    (–10, –7)
S o l u t i o n :
(i) Ordinate of (4,0) = 0
(ii) Ordinate of (5,2) =2
(iii) Ordinate of (1,-4) =- 4
(iv) Ordinate of (-10,-7) = -7
Q u e s t i o n : 3
On a graph paper, plot each of the following points:
(i)      A (4, 3)
(ii)     B (–2, 5)
(iii)    C (0, 4)
(iv)    D (7, 0)
(v)     E (–3, –5)
(vi)    F (5, –3)
(vii)   G (–5, –5)
(viii)  H (0, 0)
S o l u t i o n :
Q u e s t i o n : 4
Plot each of the following points on a graph sheet. Verify that they lie on a line.
(i)      A (4, 0),  B (4, 2), C (4, 2.5), and D (4, 6)
(ii)     P (1, 1),  Q (2, 2), R (3, 3), and S (4,4)
(iii)    L (6, 2),  M (5, 3), N (3, 5), and O (2, 6)
S o l u t i o n :
(i) After joining points A, B, C, D, we can see that the given points forms a straight line
(ii) After joining points P, Q ,R, S, we can see that the given points forms a straight line
(iii) After joining points L, M, N, O,  we can see that the given points forms a straight line
Q u e s t i o n : 5
Plot the given points on a graph sheet and check if they lie on a straight line. If not, name the shape they form
when joined in the given order.
(i)      A (0, 2),  B (0, 3.5), C (0, 5) and D (0, 6)
(ii)     P (1, 3),  Q (1, 5), R (3, 3) and S (3, 5)
(iii)    E (4, 5),  F (5, 5), G (5, 7) and H (6, 5)
(iv)    L (2, 0),  M (2, 3), N (0, 3) and O (0, 0)
(v)     J (4, 3),  K (6, 1), L (6, 5) and M (4, 7)
S o l u t i o n :
(i) After joining the given points, we see that they form a straight line.
(ii) After joining the given points, we see that they form a square.
(iii) After joining the given points, we see that they form a traingle.
Page 5


Q u e s t i o n : 1
Write the abscissa of each of the following points:
(i)     (0, 5)
(ii)    (3, 7)
(iii)   (–2, 4)
(iv)   (6, –3)
S o l u t i o n :
(i) Abscissa of (0,5) = 0
(ii) Abscissa of (3,7) =3
(iii) Abscissa of (-2,4) = -2
(iv) Abscissa of (6,-3) = 6
Q u e s t i o n : 2
Write the ordinate of each of the following points:
(i)     (4, 0)
(ii)    (5, 2)
(iii)   (1, –4)
(iv)    (–10, –7)
S o l u t i o n :
(i) Ordinate of (4,0) = 0
(ii) Ordinate of (5,2) =2
(iii) Ordinate of (1,-4) =- 4
(iv) Ordinate of (-10,-7) = -7
Q u e s t i o n : 3
On a graph paper, plot each of the following points:
(i)      A (4, 3)
(ii)     B (–2, 5)
(iii)    C (0, 4)
(iv)    D (7, 0)
(v)     E (–3, –5)
(vi)    F (5, –3)
(vii)   G (–5, –5)
(viii)  H (0, 0)
S o l u t i o n :
Q u e s t i o n : 4
Plot each of the following points on a graph sheet. Verify that they lie on a line.
(i)      A (4, 0),  B (4, 2), C (4, 2.5), and D (4, 6)
(ii)     P (1, 1),  Q (2, 2), R (3, 3), and S (4,4)
(iii)    L (6, 2),  M (5, 3), N (3, 5), and O (2, 6)
S o l u t i o n :
(i) After joining points A, B, C, D, we can see that the given points forms a straight line
(ii) After joining points P, Q ,R, S, we can see that the given points forms a straight line
(iii) After joining points L, M, N, O,  we can see that the given points forms a straight line
Q u e s t i o n : 5
Plot the given points on a graph sheet and check if they lie on a straight line. If not, name the shape they form
when joined in the given order.
(i)      A (0, 2),  B (0, 3.5), C (0, 5) and D (0, 6)
(ii)     P (1, 3),  Q (1, 5), R (3, 3) and S (3, 5)
(iii)    E (4, 5),  F (5, 5), G (5, 7) and H (6, 5)
(iv)    L (2, 0),  M (2, 3), N (0, 3) and O (0, 0)
(v)     J (4, 3),  K (6, 1), L (6, 5) and M (4, 7)
S o l u t i o n :
(i) After joining the given points, we see that they form a straight line.
(ii) After joining the given points, we see that they form a square.
(iii) After joining the given points, we see that they form a traingle.
(iv) After joining the  given points, we see that they form a rectangle.
(v) After joining the given points, we see that they form a paralellogram.
Q u e s t i o n : 6
Locate the points A (1, 2), B (4, 2) and C (1, 4) on a graph sheet taking suitable axes. Write the coordinates of the
fourth point D in order to complete the rectangle ABCD.
S o l u t i o n :
Co-ordinates of D = (4,4)