Ex. 1Multiple choice
The points (other than origin) for which abscissa is equal to the ordinate will lie in
- (A)I quadrant only
- (B)I and II quadrants
- (C)I and III quadrants
- (D)II and IV quadrants
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Solution : Answer (C)
Chapter 3 – Coordinate Geometry
Class 9 Mathematics · 40 questions · 37 with answers
Solved examples
Ex. 1Multiple choiceExercise 3.1
Write whether the following statements are True or False? Justify your answer.
- (i)Point (0, –2) lies on y-axis.
- (ii)The perpendicular distance of the point (4, 3) from the x-axis is 4.
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Solution : (i) True, because a point on the y-axis is of the form (0, y). (ii) False, because the perpendicular distance of a point from the x-axis is its ordinate. Hence it is 3, not 4.
Ex. 1Short answerExercise 3.2
Plot the point P (– 6, 2) and from it draw PM and PN as perpendiculars to x-axis and y-axis, respectively. Write the coordinates of the points M and N.
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Solution : Fig. 3.3 COORDINATE GEOMETRY 29 From the graph, we see that M(– 6, 0) and N(0, 2).
Ex. 2Multiple choiceExercise 3.2
From the Fig. 3.4, write the following:
- (i)Coordinates of B, C and E
- (ii)The point identified by the coordinates (0, – 2)
- (iii)The abscissa of the point H
- (iv)The ordinate of the point D
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Solution : (i) B = (–5, 2), C(–2, –3), E = (3, –1) (ii) F Fig. 3.4 (iii) 1 (iv) 0
Ex. 1Short answerExercise 3.3
Three vertices of a rectangle are (3, 2), (– 4, 2) and (– 4, 5). Plot these points and find the coordinates of the fourth vertex.
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Solution : Plot the three vertices of the rectangle as A(3, 2), B(– 4, 2), C(– 4, 5) (see Fig. 3.7). Fig. 3.7 We have to find the coordinates of the fourth vertex D so that ABCD is a rectangle. Since the opposite sides of a rectangle are equal, so the abscissa of D should be equal to abscissa of A, i.e., 3 and the ordinate of D should be equal to the ordinate of C, i.e., 5. So, the coordinates of D are (3, 5).
Questions
Point (–3, 5) lies in the
- (A)first quadrant
- (B)second quadrant
- (C)third quadrant
- (D)fourth quadrant
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(B) second quadrant
Signs of the abscissa and ordinate of a point in the second quadrant are respectively
- (A)+, +
- (B)–, –
- (C)–, +
- (D)+, –
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(C) –, +
Point (0, –7) lies
- (A)on the x –axis
- (B)in the second quadrant
- (C)on the y-axis
- (D)in the fourth quadrant
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(C) on the y-axis
Point (– 10, 0) lies
- (A)on the negative direction of the x-axis
- (B)on the negative direction of the y-axis
- (C)in the third quadrant
- (D)in the fourth quadrant
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(A) on the negative direction of the x-axis
Abscissa of all the points on the x-axis is
- (A)0
- (B)1
- (C)2
- (D)any number
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(D) any number
Ordinate of all points on the x-axis is
- (A)0
- (B)1
- (C)– 1
- (D)any number
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(A) 0
The point at which the two coordinate axes meet is called the
- (A)abscissa
- (B)ordinate
- (C)origin
- (D)quadrant
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(C) origin
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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(C) III quadrant
Points (1, – 1), (2, – 2), (4, – 5), (– 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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(D) do not lie in the same quadrant
If y coordinate of a point is zero, then this point always lies
- (A)in I quadrant
- (B)in II quadrant
- (C)on x - axis
- (D)on y - axis
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(C) on x - axis
The points (–5, 2) and (2, – 5) lie in the
- (A)same quadrant
- (B)II and III quadrants, respectively
- (C)II and IV quadrants, respectively
- (D)IV and II quadrants, respectively
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(C) II and IV quadrants, respectively
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has
- (A)x coordinate = – 5
- (B)y coordinate = 5 only
- (C)y coordinate = – 5 only
- (D)y coordinate = 5 or –5
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(D) y coordinate = 5 or –5
On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO which of the following figure is obtained?
- (A)Square
- (B)Rectangle
- (C)Trapezium
- (D)Rhombus
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(B) Rectangle
If P (– 1, 1), Q (3, – 4), R(1, –1), S(–2, –3) and T (– 4, 4) are plotted on the graph paper, then the point(s) in the fourth quadrant are
- (A)P and T
- (B)Q and R
- (C)Only S
- (D)P and R
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(B) Q and R
If the coordinates of the two points are P (–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is
- (A)– 5
- (B)1
- (C)– 1
- (D)– 2
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(B) 1
If P (5, 1), Q (8, 0), R (0, 4), S (0, 5) and O (0, 0) are plotted on the graph paper, then the point(s) on the x-axis are
- (A)P and R
- (B)R and S
- (C)Only Q
- (D)Q and O
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(D) Q and O
Abscissa of a point is positive in
- (A)I and II quadrants
- (B)I and IV quadrants
- (C)I quadrant only
- (D)II quadrant only COORDINATE GEOMETRY 27
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(B) I and IV quadrants
The points whose abscissa and ordinate have different signs will lie in
- (A)I and II quadrants
- (B)II and III quadrants
- (C)I and III quadrants
- (D)II and IV quadrants
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(D) II and IV quadrants
In Fig. 3.1, coordinates of P are
This question refers to a figure in the original PDF.
- (A)(– 4, 2)
- (B)(–2, 4)
- (C)(4, – 2)
- (D)(2, – 4)
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(B) (–2, 4)
In Fig. 3.2, the point identified by the coordinates (–5, 3) is Fig. 3.1
This question refers to a figure in the original PDF.
- (A)T
- (B)R
- (C)L
- (D)S
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(C) L
The point whose ordinate is 4 and which lies on y-axis is
- (A)(4, 0)
- (B)(0, 4)
- (C)(1, 4)
- (D)(4, 2)
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(B) (0, 4)
Which of the points P(0, 3), Q(1, 0), R(0, – 1), S(–5, 0), T(1, 2) do not lie on the x-axis?
- (A)P and R only
- (B)Q and S only
- (C)P, R and T
- (D)Q, S and T
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(C) P, R and T
The point which lies on y-axis at a distance of 5 units in the Fig. 3.2 negative direction of y-axis is
This question refers to a figure in the original PDF.
- (A)(0, 5)
- (B)(5, 0)
- (C)(0, – 5)
- (D)(– 5, 0)
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(C) (0, – 5)
The perpendicular distance of the point P (3, 4) from the y-axis is
- (A)3
- (B)4
- (C)5
- (D)7
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(A) 3
Write whether the following statements are True or False? Justify your answer.
- (i)Point (3, 0) lies in the first quadrant.
- (ii)Points (1, –1) and (–1, 1) lie in the same quadrant.
- (iii)The coordinates of a point whose ordinate is − and abscissa is 1 are − ,1 .
- (iv)A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0). (v) (–1, 7) is a point in the II quadrant.
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(i) Point (3, 0) lies in the first quadrant.
(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.
(iii) The coordinates of a point whose ordinate is − and abscissa is 1 are − ,1 .
(iv) A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0). (v) (–1, 7) is a point in the II quadrant.
Write the coordinates of each of the points P, Q, R, S, T and O from the Fig. 3.5. Fig. 3.5
This question refers to a figure in the original PDF.
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P(1, 1), Q(–3, 0), R(–3, –2), S(2,1), T(4, –2), O(0,0)
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)
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Trapezium
Plot the points (x, y) given by the following table: x 2 4 –3 –2 3 0 y 4 2 0 5 –3 0
Plot the following points and check whether they are collinear or not :
- (i)(1, 3), (– 1, – 1), (– 2, – 3)
- (ii)(1, 1), (2, – 3), (– 1, – 2)
- (iii)(0, 0), (2, 2), (5, 5)
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(i) (1, 3), (– 1, – 1), (– 2, – 3)
(ii) (1, 1), (2, – 3), (– 1, – 2)
(iii) (0, 0), (2, 2), (5, 5)
Without plotting the points indicate the quadrant in which they will lie, if
- (i)ordinate is 5 and abscissa is – 3
- (ii)abscissa is – 5 and ordinate is – 3
- (iii)abscissa is – 5 and ordinate is 3
- (iv)ordinate is 5 and abscissa is 3
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(i) ordinate is 5 and abscissa is – 3
(ii) abscissa is – 5 and ordinate is – 3
(iii) abscissa is – 5 and ordinate is 3
(iv) ordinate is 5 and abscissa is 3
In Fig. 3.6, LM is a line parallel to the y-axis at a distance of 3 units.
This question refers to a figure in the original PDF.
- (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?
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(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?
In which quadrant or on which axis each of the following points lie? (– 3, 5), (4, – 1), (2, 0), (2, 2), (– 3, – 6)
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II, IV, x-axis, I, III
Which of the following points lie on y-axis? A (1, 1), B (1, 0), C (0, 1), D (0, 0), E (0, – 1), F (– 1, 0), G (0, 5), H (– 7, 0), I (3, 3). Fig. 3.6
This question refers to a figure in the original PDF.
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C, D, E, G
Plot the points (x, y) given by the following table. Use scale 1 cm = 0.25 units x 1.25 0.25 1.5 – 1.75 y – 0.5 1 1.5 – 0.25 COORDINATE GEOMETRY 31
A point lies on the x-axis at a distance of 7 units from the y-axis. What are its coordinates? What will be the coordinates if it lies on y-axis at a distance of –7 units from x-axis?
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(7, 0), (0, –7)
Find the coordinates of the point
- (i)which lies on x and y axes both.
- (ii)whose ordinate is – 4 and which lies on y-axis.
- (iii)whose abscissa is 5 and which lies on x-axis.
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(i) which lies on x and y axes both.
(ii) whose ordinate is – 4 and which lies on y-axis.
(iii) whose abscissa is 5 and which lies on x-axis.
Taking 0.5 cm as 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)
Points A (5, 3), B (– 2, 3) and D (5, – 4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.
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C(–2, – 4)
Write the coordinates of the vertices of a rectangle whose length and breadth are
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(0, 0), (–5, 0), (0, –3)
and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant. 3. Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS is a square. 4. From the Fig. 3.8, answer the following :
This question refers to a figure in the original PDF.
- (i)Write the points whose abscissa is 0.
- (ii)Write the points whose ordinate is 0.
- (iii)Write the points whose abscissa is – 5. 5. Plot the points A (1, – 1) and B (4, 5) (i) Draw a line segment joining these points. Write the coordinates of a point on this line Fig. 3.8 segment between the points A and B. (ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB.
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(i) Write the points whose abscissa is 0.
(ii) Write the points whose ordinate is 0.