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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Additional Questions

Exercise 5.1

Question 1.
State whether the following statements are true/false.
(i) (5, 7) is a point in the IV quadrant.
(ii) (-2, -7) is a point in the III quadrant.
(iii) (8, -7) lies below the x-axis.
(iv) (-2, 3) lies in the II quadrant.
(v) For any point on the x-axis its y-coordinate is zero.
Solution:
(i) False
(ii) True
(iii) True
(iv) True
(v) True

Question 2.
Locate the points
(i) (3, 5) and (5, 3)
(ii) (-2, -5) and (-5, -2) in the rectangular coordinate system.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 1

Question 3.
In which quadrant does the following points lie?
(i) (5, 2)
(ii) (-5, -8)
(iii) (-7, 1)
(iv) (8, -3)
Solution:
(i) I quadrant
(ii) III quadrant
(iii) II quadrant
(iv) IV quadrant.

Question 4.
Write down the ordinate of the following points.
(i) (7, 5)
(ii) (2, 9)
(iii) (-5, 8)
(iv) (7, -4)
Solution:
(i) 5
(ii) 9
(iii) 8
(iv) -4 (ordinate is the y-coordinate)

Exercise 5.2

Question 1.
Find the distance between the following pairs of points.
(i) (-4, 0) and (3, 0)
(ii) (-7, 2) and (5, 2)
Solution:
(i) The points (-4, 0) and (3, 0) lie on the x-axis. Hence,
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 2
(ii) The points (5,2) and (-7,2) lie on a line parallel to the x-axis. Hence the distance
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 60

Question 2.
Show that the three points (4, 2), (7, 5) and (9, 7) lie on a straight line.
Solution:
Let the points be A(4, 2), B(7, 5) and C(9, 7). By the distance formula.
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 61
Hence the points A, B and C are collinear.

Question 3.
Determine whether the points are vertices of a right triangle A(-3, -4), B(2, 6) and C (-6, 10).
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 62
Hence ABC is a right angled triangle since the square of one side is equal to sum of the squares of the other two sides.

Question 4.
Show that the points (a, a), (-a, -a) and (\(-a \sqrt{3}, a \sqrt{3}\)) form an equilateral triangle.
Solution:
Let the points be represented by A (a, a), B(-a, -a) and C(\(-a \sqrt{3}, a \sqrt{3}\)) using the distance formula.
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 63
Since all the sides are equal the points form an equilateral triangle.

Question 5.
Prove that the points (-7, -3), (5, 10), (15, 8) and (3, -5) taken in order are the corners of a parallelogram.
Solution:
Let A, B, C and D represent the points (-7, -3), (5, 10), (15, 8) and (3, -5) respectively.
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 64
i.e. The opposite sides are equal. Hence ABCD is a parallelogram.

Question 6.
Show that the following points A (3, 1) B(6, 4) and C(8, 6) lies on a straight line. Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 65
Solution:
Using the distance formula, we have
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 66
Therefore the points lie on a straight line.

Question 7.
If the distance between the points (5, -2), (1, a) is 5 units. Find the value of a.
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 67
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 68

Exercise 5.3

Question 1.
A, B and C are vertices of ∆ ABC. D, E and F are mid points of sides AB, BC and AC respectively. If the coordinates of A, D and F are (-3, 5), (5, 1) and (-5, -1) respectively. Find the coordinates of B, C and E.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 70

Question 2.
If A(10, 11) and B(2, 3) are the coordinates of end points of diameter of circle. Then find the centre of the circle.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 80

Question 3.
Find the coordinates of the point which divides the line segment joining the points (3, 1) and (5, 13) internally in the ratio 3 : 5.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 90

Exercise 5.4

Question 1.
Using section formula, show that the points A(7, -5), B(9, -3) and C(13, 1) are collinear.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 91

Question 2.
A car travels at an uniform speed. At 2pm it is at a distance of 5 km at 6 pm it is at a distance of 120 km. Using section formula, find at what distance it will reach 2 mid night.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 92

Question 3.
Find the coordinates of the point which divides the line segment joining the point A(3, 7) and B(-11, -2) in the ratio 5 : 1.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 93

Exercise 5.5

Question 1.
Find the centroid of the triangle whose vertices are (2, -5), (5, 11) and (9, 9)
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 94

Question 2.
If the centroid of a triangle is at (10, -1) and two of its vertices are (3, 2) and (5, -11). Find the third vertex of the triangle.
Solution:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 95

Exercise 5.6

Multiple Choice Questions :

Question 1.
The point (-2, 7) lies is the quadrant
(1) I
(2) II
(3) III
(4) IV
Hint:
(-, +) lies in IInd quadrant
Solution:
(2) II

Question 2.
The point (x, 0) where x < 0 lies on
(1) OX
(2) OY
(3) OX’
(4) OY’
Hint:
(-, 0) lies on OX’
Solution:
(3) OX’

Question 3.
For a point A(a, b) lying in quadrant III.
(1) a > 0, b < 0
(2) a < 0, b < 0
(3) a > 0, b > 0
(4) a < 0, b > 0
Hint:
(-, -) lies in IIIrd quadrant
Solution:
(2) a < 0, b < 0

Question 4.
The diagonal of a square formed by the points (1, 0) (0, 1) and (-1, 0) is
(1) 2
(2) 4
(3) \(\sqrt{2}\)
(4) 8
Hint:
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 50
Solution:
(1) 2

Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Additional questions

Question 5.
The triangle obtained by joining the points A(-5, 0) B(5, 0) and C(0, 6) is
(1) an isosceles triangle
(2) right triangle
(3) scalene triangle
(4) an equilateral triangle
Hint:
Triangles having two sides equal are called isosceles.
Solution:
(a) an isosceles triangle

Text Book Activities

Activity 1.
Plot the following points on a graph sheet by taking the scale as 1cm = 1 unit. Find how far the points are from each other? A (1, 0) and D (4, 0). Find AD and also DA. Is AD = DA? You plot another set of points and verify your result.
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 99
Solution:
AD = DA is correct.
Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Additional Questions 100

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