#### Chapters

## Chapter 5: Coordinate Geometry

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.1 [Pages 192 - 193]

Plot the following point in the coordinate system and identify the quadrant.

P(−7, 6)

Plot the following point in the coordinate system and identify the quadrant.

Q(7, −2)

Plot the following point in the coordinate system and identify the quadrant.

R(−6, −7)

Plot the following point in the coordinate system and identify the quadrant.

S(3, 5)

Plot the following point in the coordinate system and identify the quadrant.

T(3, 9)

Write down the abscissa and ordinate of the following.

P

Write down the abscissa and ordinate of the following.

Q

Write down the abscissa and ordinate of the following.

R

Write down the abscissa and ordinate of the following.

S

Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure?

(−5, 3) (−1, 3) (0, 3) (5, 3)

Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure?

(0, −4) (0, −2) (0, 4) (0, 5)

Plot the following points in the coordinate plane. Join them in order. What type of geometrical shape is formed?

(0, 0) (−4, 0) (−4, −4) (0, −4)

Plot the following points in the coordinate plane. Join them in order. What type of geometrical shape is formed?

(−3, 3) (2, 3) (−6, −1) (5, −1)

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.2 [Pages 202 - 203]

Find the distance between the following pair of points

(1, 2) and (4, 3)

Find the distance between the following pair of points

(3, 4) and (−7, 2)

Find the distance between the following pair of points

(a, b) and (c, b)

Find the distance between the following pair of points

(3, −9) and (−2, 3)

Determine whether the given set of points are collinear or not

(7, −2), (5, 1), (3, 4)

Determine whether the given set of points are collinear or not

(a, −2), (a, 3), (a, 0)

Show that the following points taken in order to form an isosceles triangle

A(5, 4), B(2, 0), C(−2, 3)

Show that the following points taken in order to form an isosceles triangle

A(6, −4), B(−2, −4), C(2, 10)

Show that the following points taken in order to form an equilateral triangle

`"A"(2, 2), "B"(-2, -2), "C"(-2sqrt(3), 2sqrt(3))`

Show that the following points taken in order to form an equilateral triangle

`"A"(sqrt(3), 2), "B"(0, 1), "C"(0, 3)`

Show that the following points taken in order to form the vertices of a parallelogram

A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)

Show that the following points taken in order to form the vertices of a parallelogram

A(−7, −3), B(5, 10), C(15, 8) and D(3, −5)

Verify that the following points taken in order to form the vertices of a rhombus

A(3, −2), B(7, 6), C(−1, 2) and D(−5, −6)

Verify that the following points taken in order to form the vertices of a rhombus

A(1, 1), B(2, 1), C(2, 2) and D(1, 2)

A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’

The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?

The point (x, y) is equidistant from the points (3, 4) and (−5, 6). Find a relation between x and y

Let A(2, 3) and B(2, −4) be two points. If P lies on the x-axis, such that AP = `3/7` AB, find the coordinates of P.

Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)

The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.3 [Page 208]

Find the mid-point of the line segment joining the points

(−2, 3) and (−6, −5)

Find the mid-point of the line segment joining the points

(8, −2) and (−8, 0)

Find the mid-point of the line segment joining the points

(a, b) and (a + 2b, 2a – b)

Find the mid-point of the line segment joining the points

`(1/2, (-3)/7)` and `(3/2, (-11)/7)`

The centre of a circle is (−4, 2). If one end of the diameter of the circle is (−3, 7) then find the other end

If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0, then what will be the value of p?

The mid-point of the sides of a triangle are (2, 4), (−2, 3) and (5, 2). Find the coordinates of the vertices of the triangle

O(0, 0) is the centre of a circle whose one chord is AB, where the points A and B are (8, 6) and (10, 0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD.

The points A(−5, 4), B(−1, −2) and C(5, 2) are the vertices of an isosceles right-angled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square

The points A(−3, 6), B(0, 7) and C(1, 9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallelogram.

A(−3, 2), B(3, 2) and C(−3, −2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.4 [Page 214]

Find the coordinates of the point which divides the line segment joining the points A(4, −3) and B(9, 7) in the ratio 3 : 2

In what ratio does the point P(2, −5) divide the line segment joining A(−3, 5) and B(4, −9)

Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) in such a way that AP = `2/5` AB

Find the coordinates of the points of trisection of the line segment joining the points A(−5, 6) and B(4, −3)

The line segment joining A(6, 3) and B(−1, −4) is doubled in length by adding half of AB to each end. Find the coordinates of the new end points.

Using section formula, show that the points A(7, −5), B(9, −3) and C(13, 1) are collinear

A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2, −3) and (2, 1) respectively, then find the coordinates of C.

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.5 [Pages 217 - 218]

Find the centroid of the triangle whose vertices are (2, −4), (−3, −7) and (7, 2)

Find the centroid of the triangle whose vertices are (−5, −5), (1, −4) and (−4, −2)

If the centroid of a triangle is at (4, −2) and two of its vertices are (3, −2) and (5, 2) then find the third vertex of the triangle

Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1)

The vertices of a triangle are (1, 2), (h, −3) and (−4, k). If the centroid of the triangle is at the point (5, −1) then find the value of `sqrt(("h" + "k")^2 + ("h" + 3"k")^2`

Orthocentre and centroid of a triangle are A(−3, 5) and B(3, 3) respectively. If C is the circumcentre and AC is the diameter of this circle, then find the radius of the circle

ABC is a triangle whose vertices are A(3, 4), B(−2, −1) and C(5, 3). If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

If `(3/2, 5), (7, (-9)/2)` and `(13/2, (-13)/2)` are mid-points of the sides of a triangle, then find the centroid of the triangle

### Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.6 [Pages 218 - 219]

#### Multiple Choice Questions

If the y-coordinate of a point is zero, then the point always lies ______

in the I quadrant

in the II quadrant

on x-axis

on y-axis

The points (−5, 2) and (2, −5) lie in the ________

same quadrant

II and III quadrant respectively

II and IV quadrant respectively

IV and II quadrant respectively

On plotting the points O(0, 0), A(3, −4), B(3, 4) and C(0, 4) and joining OA, AB, BC and CO, which of the following figure is obtained?

Square

Rectangle

Trapezium

Rhombus

If P(−1, 1), Q(3, −4), R(1, −1), S(−2, −3) and T(−4, 4) are plotted on a graph paper, then the points in the fourth quadrant are __________

P and T

Q and R

only S

P and Q

The point whose ordinate is 4 and which lies on the y-axis is _______________

(4, 0)

(0, 4)

(1, 4)

(4, 2)

The distance between the two points (2, 3) and (1, 4) is ______

2

`sqrt(56)`

`sqrt(10)`

`sqrt(2)`

If the points A(2, 0), B(– 6, 0), C(3, a – 3) lie on the x-axis then the value of a is _____

0

2

3

– 6

If (x + 2, 4) = (5, y – 2), then the coordinates (x, y) are _____

(7, 12)

(6, 3)

(3, 6)

(2, 1)

If Q_{1}, Q_{2}, Q_{3}, Q_{4} are the quadrants in a Cartesian plane then Q_{2} ∩ Q_{3} is ___________

Q

_{1}U Q_{2}Q

_{2}U Q_{3}Null set

Negative x-axis

The distance between the point (5, −1) and the origin is _________

`sqrt(24)`

`sqrt(37)`

`sqrt(26)`

`sqrt(17)`

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2 : 1 is

`(7/2, 11/2)`

(3, 5)

(4, 4)

(4, 6)

If `"P"("a"/3, "b"/2)` is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is

(−9, 7)

`(-3, 7/2)`

(9, −7)

`(3, -7/2)`

In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3)

1 : 2

2 : 1

1 : 3

3 : 1

If the coordinates of one end of a diameter of a circle is (3, 4) and the coordinates of its centre is (−3, 2), then the coordinate of the other end of the diameter is

(0, −3)

(0, 9)

(3, 0)

(−9, 0)

The ratio in which the x-axis divides the line segment joining the points A (a_{1}, b_{1}) and B (a_{2}, b_{2}) is

b

_{1}: b_{2}−b

_{1}: b_{2}a

_{1}: a_{2}−a

_{1}: a_{2}

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is

2 : 3

3 : 4

4 : 7

4 : 3

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are

(3, 2), (2, 4)

(4, 0), (2, 8)

(3, 4), (2, 0)

(4, 3), (2, 4)

The mid-point of the line joining (−a, 2b) and (−3a, −4b) is

(2a, 3b)

(−2a, −b)

(2a, b)

(−2a, −3b)

In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally

1 : 3

2 : 5

3 : 1

5 : 2

If (1, −2), (3, 6), (x, 10) and (3, 2) are the vertices of the parallelogram taken in order, then the value of x is

6

5

4

3

## Chapter 5: Coordinate Geometry

## Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board chapter 5 - Coordinate Geometry

Samacheer Kalvi solutions for Mathematics Class 9th Tamil Nadu State Board chapter 5 (Coordinate Geometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Mathematics Class 9th Tamil Nadu State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Class 9th Tamil Nadu State Board chapter 5 Coordinate Geometry are Plotting a Point in the Plane If Its Coordinates Are Given., Concept for Mapping the Space Around Approximately Through Visual Estimation., Co-ordinates of Points and Distance, Cartesian System, The Mid-point of a Line Segment (Mid-point Formula), Points of Trisection of a Line Segment (Mid-point Formula), Section Formula, The Coordinates of the Centroid.

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