Similarity - Test Questions

Question 1

Question:   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)

Answer:   

Question 2

Question:   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)

Answer:   

Question 3

Question:   (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.

Answer:   

Question 4

Question:   (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?

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.

Question 5

Question:   (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.

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

Question 6

Question:   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.

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

Question 7

Question:   Plot the points (3, 1), (4, 3), (0, 3) and (-1, 1) on a graph paper. Name the figure formed and find its area.

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

Question 8

Question:   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.

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.

Question 9

Question:   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.

Answer:   

The coordinates of the vertices of the rhombus ABCD are:
A (4, 0), B (0, 3), C (-4, 0), D (0, 3)

Question 10

Question:   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?

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)