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Question (1):
Plot the following points on a graph paper:
(a) A (+4, +3)
(b) B (+2, -3)
(c) C (-5, +1)
(d) D (-4, -2)
(e) E (+4, 0)
(f) F (-3, 0)
(g) G (0, -4)
(h) H (0, +3)
(i) I (0, 0)
(j) J (-2, -2)
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Answer:
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Question (2):
Plot the following points on a graph paper:
(a) 
(b) 
(c) 
(d) 
(e) 
(f) (0, 2.5)
(g) (-1.5, 4.5)
(h) (-3, 3.5)
(i) (2.25, -3.75)
(j) (4.2, -1.8)
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Answer:
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Question (3):
(a) Plot a point P on the graph paper whose abscissa is 4 and ordinate is 3.
(b) Plot a point Q on the graph paper whose abscissa is -3 and ordinate is -2.5.
(c) Plot a point R on the graph paper whose abscissa is zero and ordinate is 4.
(d) Plot a point M on the graph paper whose abscissa is -2 and ordinate is zero.
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Answer:
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Question (4):
(a) A point P is on the X-axis and 3 units from the origin. State its abscissa and ordinate.
(b) A point Q is on the Y-axis. State its abscissa and ordinate if Q is 4 units from the origin.
(c) The abscissa of a point M is (2a) and the ordinate is (-4a). In which quadrant the point M lies if 'a' is a positive real number?
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Answer:
(a) P is on the X axis
\ Its ordinate is zero.
It is 3 units from the origin on the X axis.
\ Its abscissa is 3 or -3.
The abscissa and ordinate of P are 3 and 0 respectively or -3 and 0 respectively.
(b) Q is on the Y axis
\ Its abscissa is zero.
It is 4 units from the origin on the Y axis.
\ Its ordinate is 4 or -4.
The abscissa and ordinate of Q are 0 and 4 respectively or 0 and -4 respectively.
(c) The abscissa of M has a positive value and the ordinate of M has a negative value.
\ M lies in the fourth quadrant.
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Question (5):
(a) A right angled triangle ABC has its vertices A (4, 0), B (0, 0) and C (0, 2). Plot the points on a graph paper and find the area of the triangle.
(b) Plot the following points on a graph paper and name the figure formed: P (5, -3), Q (5, 0), R (2, 0). Find its area.
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Answer:
(a)
Area of DABC 
Area = 4 square units
(b)
The figure formed is an isosceles right angled triangle.
It is DPQR, with PQ = QR = 3 units and 
Area of DPQR 
Area = 4.5 square units
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Question (6):
The points (-3, 0), (0, 0), (0, -3) and (-3, 3) are the vertices of a quadrilateral. Give the special name of the quadrilateral and find its perimeter and area.
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Answer:
The quadrilateral formed is a square (Since the length of each is 3 units and the sides are perpendicular to each other).
Perimeter of Square OABC = 4 x 3 = 12 units
Area of Square OABC = 32 = 9 square units
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Question (7):
Plot the points (3, 1), (4, 3), (0, 3) and (-1, 1) on a graph paper. Name the figure formed and find its area.
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Answer:
The figure formed is a parallelogram since both the pairs of opposite sides are parallel.
From the graph,
Height of the parallelogram = 2 units
Base of the parallelogram = 4 units
Area of parallelogram = base x height
= 4 x 2
= 8 square units
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Question (8):
The coordinates of a quadrilateral are (2, 2), (-2, 2), (-2, -2) and (2, -2). What type of quadrilateral is it? Find its perimeter and area.
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Answer:
The quadrilateral is a square, since all sides are equal and each angle is a right angle.
Perimeter of square ABCD = 4 x 4 units = 16 units.
Area of square ABCD = 42 = 16 square units.
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Question (9):
The diagonals of a rhombus ABCD are along the X-axis and the Y-axis. Point A is 4 units from the origin and is on the positive side of the X-axis, whereas B is 3 units from the origin. Find the coordinates of the vertices of the rhombus ABCD.
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Answer:
The coordinates of the vertices of the rhombus ABCD are:
A (4, 0), B (0, 3), C (-4, 0), D (0, 3)
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Question (10):
One of the vertices of a square is (3, 3). If two of its sides are along the X-axis and the Y-axis respectively. What are the coordinates of the vertices of the square?
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Answer:
Let OABC be the square formed.
The coordinates of the vertices of the square are:
O (0, 0), A (3, 0), B (3, 3), C (0, 3)
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Question (11):
Plot the following points on a graph sheet. A(1,3), B(2,6), C(3,9), D(4,12). Do the points lie on a straight line? Does the line, joining A and B passes through the origin?
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Answer:
The points lie on a straight line.
The line joining A and B passes through the origin.
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Question (12):
The coordinates of 3 vertices of a rectangle are given. By plotting the given points, find the coordinates of the fourth vertex. B(10, 4), C(0, 4), D(0, -2).
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Answer:
From the graph, the coordinates of the fourth vertex A are (10, -2).
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Question (13):
A (-2, 2), B (8, 2), C (4, -4) are the three vertices of a parallelogram ABCD. Plot the points on a graph paper and find its fourth vertex D. Also, from the same graph, state the coordinates of the midpoints of the sides AB and CD.
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Answer:
From the graph, the coordinates of the fourth vertex D of the parallelogram ABCD are (-6, -4).
Let P be the midpoint of side AB.
Then, coordinates of P are (3, 2).
Let Q be the midpoint of side CD.
Then, coordinates of Q are (-1, -4).
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Question (14):
A (-2, 4), C (4, 10) and D (-2, 10) are the vertices of a square ABCD. Use graphical method to find the coordinates of the fourth vertex B. Also, find
(i) the coordinates of the midpoint of BC
(ii) the coordinates of the midpoint of CD and
(iii) the coordinates of the point of intersection of the diagonals of the square ABCD.
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Answer:
From the graph, the coordinates of the fourth vertex B are (4, 4).
(i) Let P be the midpoint of BC. P has coordinates (4, 7).
(ii) Let Q be the midpoint of CD. Q has coordinates (1, 10).
(iii) Let E be the point of intersection of the diagonals AC and BD. E has coordinates (1, 7).
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Question (15):
Draw a pair of axes,
(a) Plot the points (4, 1), (1, 3) and (-1, 0).
(b) A fourth point is added to make a square. What are its coordinates?
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Answer:
(a) Let the plotted points be A (4, 1), B (1, 3) and C (-1, 0).
(b) Complete the square ABCD by drawing parallel lines to AB and BC. Let the fourth point be D. From the graph, D has coordinates (2, -2).
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Question (16):
The points P (-3, 2) and Q (5, 2) are two corners of a square. What are the coordinates of the other two corners, if
(a) the square is drawn above the side PQ
(b) the square is drawn below the side PQ
(c) PQ is a diagonal of the square.
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Answer:
Plot the points P (-3, 2) and Q (5, 2).
(a)
Distance between P and Q is 8 units.
So, mark the points R and S, taking the vertical distance of 8 units upwards from Q and P respectively.
From the graph, R has coordinates (5, 10) and S has coordinates (-3, 10).
(b)
Mark the points R and S, taking the vertical distance of 8 units downwards from Q and P respectively.
From the graph, R has coordinates (5, -6) and S has coordinates (-3, -6).
(c)
Join PQ.
Mark O, the midpoint of PQ.
O is also the midpoint of the other diagonal RS. Since diagonals of a square bisect each other.
From O, taking vertical distance of 4 units upwards mark R.
From O, taking vertical distance of 4 units downwards, mark S.
From the graph, R has coordinates (1, 6) and S has coordinates (1, -2).
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Question (17):
State whether the statement is true (T) or false (F)?
(a) (-1, 0) lies on the X-axis
(b) (3, -4) lies on the Y-axis
(c) (2, -3) lies in the third quadrant
(d) (0, -4) lies on the X-axis
(e) (-3, 0) lies on the Y-axis
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Answer:
(a) T (because ordinate is zero)
(b) F (because abscissa is not zero)
(c) F (in the third quadrant, both ordinate and
abscissa are negative)
(d) F (because ordinate is not zero)
(e) F (because abscissa is not zero)
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Question (18):
For each of the following, state the quadrant in which the point lies:
(i) (3, 3)
(ii) 
(iii) (2, -4)
(iv) 
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Answer:
(i) first quadrant
(ii) second quadrant
(iii) first quadrant
(iv) third quadrant
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Question (19):
In each of the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation.
(i) 3 - 2x = 7, 2y + 1 = 10 - 
(ii) 
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Answer:
(i) 3 - 2x = 7
\ 2x = -4
x = -2 ....(1)
2y + 1 = 10 - 
9y = 18
y = 2 ....(2)
\ Coordinates of the required point are (-2, 2).
(ii) 
a = 6 ....(1)
45 - 12b = 14b - 7
26b = 52
b = 2 ....(2)
\ Coordinates of the required point are (6, 2).
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Question (20):
In the given figure, write the coordinates of the points A, B, C, D, E.
(i) What type of quadrilateral is the figure ABCD?
(ii) Find the area of the quadrilateral ABCD.
(iii) Find the area of triangle ABE.
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Answer:
A has coordinates (2, 2)
B has coordinates (7, 2)
C has coordinates (8, 4)
D has coordinates (3, 4)
(i) The figure ABCD is a parallelogram, since one pair of opposite sides is parallel and equal (AB||DC, AB = DC).
(ii) Area of ABCD = base x height
= 5 x 2
= 10 square units
(iii) Area of DABE = 
= 
= 5 square units
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