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Question 11
Question: 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?
Answer:
The points lie on a straight line.
The line joining A and B passes through the origin.
Question 12
Question: 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).
Answer:
From the graph, the coordinates of the fourth vertex A are (10, -2).
Question 13
Question: 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.
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).
Question 14
Question: 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.
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).
Question 15
Question: 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?
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).
Question 16
Question: 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.
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).
Question 17
Question: 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
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)
Question 18
Question: For each of the following, state the quadrant in which the point lies:
(i) (3, 3)
(ii) 
(iii) (2, -4)
(iv) 
Answer: (i) first quadrant
(ii) second quadrant
(iii) first quadrant
(iv) third quadrant
Question 19
Question: 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) 
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).
Question 20
Question: 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.
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
