Co-Ordinate Geometry

Question 1.
In a locality, there is a main road along North - South direction. The map is given below. With the help of the picture answer the following questions.

• i) What is the 3rd object on the left side in street no. 3 while going in east direction ?
• ii) Find the name of the 2nd house which is on right side of street 2 while going in east direction.
• iii) Locate the position of Mr. K’s house.
• iv) How do you describe the position of the post office ?
• v) How do you describe the location of the hospital ?
• Solution:
• i) Water tank
• ii) Mr. J’s house
• iii) In street No. 2, 3rd house on right side.
• iv) In street No. 4, the first house on right side.
• v) In street No. 4, the last house on left side.

Question 1.
Write the quadrant in which the following points lie.

• i) (- 2, 3)
• ii) (5, - 3)
• iii) (4, 2)
• iv) (- 7, - 6)
• v) (0, 8)
• vi) (3, 0)
• vii) (-4,0)
• viii) (0, – 6)
• Solution:
• i) (- 2, 3) - Q₂(second quadrant)
• ii) (5, - 3) - Q₄(fourth quadrant)
• iii) (4, 2) - Q₁(Iirst quadrant)
• iv) (- 7, - 6) - Q₃(third quadrant)
• v) (0, 8) - on Y-axis
• vi) (3, 0) - on X-axis
• vii) (-4,0) - on X’ - axis
• viii) (0, - 6) - on Y’: axis

Question 2.
Write the abscissae and ordinates of the following points.

• i)(4,-8)
• ii)(-5,3)
• iii)(0,0)
• iv)(5, 0)
• v)(0, -8)

Note: Plural of abscissa is abscissae.

Solution:

Point	abscissa	ordinate
i) (4, - 8)	4	-8
ii) (-5, 3)	-5	3
iii) (0,0)	0	0
iv) (5,0)	5	0
v) (0,-8) .	0	-8

Question 3.
Which of the following points lie on the axes ? Also name the axis.

• i) (-5,-8)
• ii) (0, 13)
• iii) (4, - 2)
• iv) (- 2,0)
• v) (0, - 8)
• vi) (7,0)
• vii) (0,0)

Solution:

The points (ii) (0,13) ; (v) (0,- 8) lie on Y - axis.
The points (iv) (- 2, 0), (vi) (7, 0) lie on X - axis.
The point (vii) (0, 0) lie on both X - axis and Y - axis.
The points (i) (- 5, - 8); (iii) (4, – 2) do not lie on any axis.

Question 4.
Write the following based on the graph.

• i) The ordinate of L
• ii) The ordinate of Q
• iii) The point denoted by (- 2,-2)
• iv) The point denoted by (5, – 4)
• v) The abscissa of N
• vi) The abscissa of M

Solution:

• i) - 7
• ii) 7
• iii) The point ’R’
• iv) The point P
• v) 4
• vi) - 3

Question 5.
State true or false and write correct statement.

• i) In the Cartesian plane the horizon-tal line is called Y - axis, if) in the Cartesian plane, the vertical line is called Y – axis.
• iii) The point which lies on both the axes is called origin.
• iv) The point (2, - 3) lies in the third quadrant.
• v) (-5, -8) lies in the fourth quadrant.
• vi) The point (- x, - y) lies in the first quadrant where x < 0; y < 0.

Solution:

i) False
Correct statement: In the Cartesian plane the horizontal line is called X – axis.
ii) True
iii) True
iv) False
Correct statement: The point (2, -3) lies in the fourth quadrant.
v) False
Correct statement: (- 5, - 8) lies in the third quadrant.
vi) True

Question 6.
Plot the following ordered pairs on a graph sheet. What do you observe ?

i) (1, 0), (3, 0), (- 2, 0), (- 5, 0), (0, 0), (5, 0), (- 6, 0)
ii) (0, 1), (0, 3), (0, – 2), (0, – 5), (0, 0), (0,5), (0,-6)

Solution:
i) All points lie on X - axis,
ii) All points lie on Y - axis.

Question 1.
Plot the following points on the Cartesian plane whose x, y co-ordinates are given.

Solution

Question 2.
Are the positions of (5, -8) and (-8, 5) Is same ? JustIfy your answer.

Solution:
The positions of (5, -8) and (-8, 5) are not same. They are two distinct points. (5, -8) lies at a distance of 5 units from Y – axis and 8 units from X – axis on down side of the origin. So it lies in Q₄. Where as (- 8, 5) lies in Q₂. The point is at a distance of 8 units from Y – axis on left side of the origin and 5 units from X – axis.

Question 3.
What can you say about the position of the points (1, 2), (1, 3), (1, – 4), (1, 0) and (1, 8), Locate on a graph sheet.

Solution:

All the given points lie on a line parallel to Y-axis at a distance of 1 cm.

Question 4.
What can you say about the position of the points (5, 4), (8, 4), (3, 4), (0, 4), (-4, 4), (-2,4)? Locate the points on a graph sheet and justify your answer.

Solution:
The points (5, 4), (8, 4), (3, 4), (0, 4), (- 4, 4) and (- 2, 4) all lie on a line parallel to X-axis at a distance of 4-units from it.

Question 5.
Plot the points (0, 3), (4, 3), (3, 4) (4, 0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle.

Solution:

From the graph, area of the rectangle =12 square units (OR)
Length = 4 units ; breadth = 3 units
A = l/b = 4 × 3 = 12 sq. units.

Question 6.
Plot the points (2, 3), (6, 3) and (4, 7) in a graph sheet. Join them to make it a triangle. Find the area of the triangle.

Solution:

From the graph
Base of the triangle = 4 units
Height of the triangle = 4 units
∴ Area of the triangle = 1/2 × base × height = 1/2 × 4 × 4 = 8sq. units.

Question 7.
Plot at least six points in a graph sheet, each having the sum of its co-ordinates equal to 5. [Hint: (- 2, 7), (1, 4)………….]

Solution:
Given that (x co-ordinate) + (y co-ordinate) = 5
Let the points be

Question 8.
Look at the graph. Write the co-ordinates of the points
A, B, C, D, E, F. G. H, 1, J, K, L, M, N, O, P and Q.

Solution:
A(- 3, 4) ; B(0, 5) : C (3, 4) ; D (2, 4) ; E (2, 0) ;
F (3, 0) ; G (3, - 1) ; H (0, - 1) ; I (- 3, - 1) ;
J (- 3, 0) ; K (- 2, 0) ; L (- 2, 4) ; M (- 1, 0) ;
N (-1, 3); O (0, 0) ; P (1. 3) and Q (1, 0)

Question 9.
In a graph sheet plot each pair of points, join them by line segments.

• i) (2, 5), (4, 7)
• ii) (-3, 5) (-1,7)
• iii) (-3, -4), (2, -4)
• iv) (-3, -5) (2, -5)
• v) (4, -2), (4, -3)
• vi) (-2, 4), (-2, 3)
• vii) (-2, 1), (-2, 0)

Now join the following pairs of points by straight line segments, in the same graph.

• viii) (-3, 5), (-3, 4)
• ix) (2, 5), (2, -4)
• x) (2, -4), (4, -2)
• xi) (2, -4), (4, -3)
• xii) (4, -2), (4, 7)
• xiii) (4, 7), (-1, 7)
• xiv) (-3, 2), (2, 2)

Now you will get a surprise figure. What is it ?

Solution: