Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board chapter 5 - Coordinate Geometry [Latest edition]

## Chapter 5: Coordinate Geometry

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4Exercise 5.5Unit Exercise – 5
Exercise 5.1 [Pages 211 - 212]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.1 [Pages 211 - 212]

Exercise 5.1 | Q 1. (i) | Page 211

Find the area of the triangle formed by the points

(1, – 1), (– 4, 6) and (– 3, – 5)

Exercise 5.1 | Q 1. (ii) | Page 211

Find the area of the triangle formed by the points

(–10, –4), (–8, –1) and (–3, –5)

Exercise 5.1 | Q 2. (ii) | Page 211

Determine whether the sets of points are collinear?

(-1/2, 3), (-5, 6) and (-8, 8)

Exercise 5.1 | Q 2. (ii) | Page 211

Determine whether the sets of points are collinear?

(a, b + c), (b, c + a) and (c, a + b)

Exercise 5.1 | Q 3. (i) | Page 211

Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.

 Vertices Area (sq.units) (0, 0), (p, 8), (6, 2) 20
Exercise 5.1 | Q 3. (ii) | Page 211

Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.

 Vertices Area (sq.units) (p, p), (5, 6), (5, –2) 32
Exercise 5.1 | Q 4. (i) | Page 212

In the following, find the value of ‘a’ for which the given points are collinear

(2, 3), (4, a) and (6, – 3)

Exercise 5.1 | Q 4. (ii) | Page 212

In the following, find the value of ‘a’ for which the given points are collinear

(a, 2 – 2a), (– a + 1, 2a) and (– 4 – a, 6 – 2a)

Exercise 5.1 | Q 5. (i) | Page 212

Find the area of the quadrilateral whose vertices are at (– 9, – 2), (– 8, – 4), (2, 2) and (1, – 3)

Exercise 5.1 | Q 5. (ii) | Page 212

Find the area of the quadrilateral whose vertices are at (– 9, 0), (– 8, 6), (– 1, – 2) and (– 6, – 3)

Exercise 5.1 | Q 6 | Page 212

Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are (– 4, – 2), (– 3, k), (3, – 2) and (2, 3)

Exercise 5.1 | Q 7 | Page 212

If the points A(– 3, 9), B(a, b) and C(4, – 5) are collinear and if a + b = 1, then find a and b

Exercise 5.1 | Q 8 | Page 212

Let P(11, 7), Q(13.5, 4) and R(9.5, 4) be the midpoints of the sides AB, BC and AC respectively of ∆ABC. Find the coordinates of the vertices A, B and C. Hence find the area of ∆ABC and compare this with area of ∆PQR.

Exercise 5.1 | Q 9 | Page 212

The quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of the patio

Exercise 5.1 | Q 10 | Page 212

A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied

Exercise 5.1 | Q 11. (i) | Page 212

Find the area of triangle AGF

Exercise 5.1 | Q 11. (ii) | Page 212

Find the area of triangle FED

Exercise 5.1 | Q 11. (iii) | Page 212

Find the area of quadrilateral BCEG

Exercise 5.2 [Pages 220 - 221]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.2 [Pages 220 - 221]

Exercise 5.2 | Q 1. (i) | Page 220

What is the slope of a line whose inclination with positive direction of x-axis is 90°

Exercise 5.2 | Q 1. (ii) | Page 220

What is the slope of a line whose inclination with positive direction of x-axis is 0°

Exercise 5.2 | Q 2. (i) | Page 220

What is the inclination of a line whose slope is 0

Exercise 5.2 | Q 2. (ii) | Page 220

What is the inclination of a line whose slope is 1

Exercise 5.2 | Q 3. (i) | Page 220

Find the slope of a line joining the points

(5, sqrt(5)) with the origin

Exercise 5.2 | Q 3. (ii) | Page 220

Find the slope of a line joining the points

(sin θ, – cos θ) and (– sin θ, cos θ)

Exercise 5.2 | Q 4 | Page 220

What is the slope of a line perpendicular to the line joining A(5, 1) and P where P is the mid-point of the segment joining (4, 2) and (– 6, 4)

Exercise 5.2 | Q 5 | Page 220

Show that the given points are collinear: (– 3, – 4), (7, 2) and (12, 5)

Exercise 5.2 | Q 6 | Page 220

If the three points (3, – 1), (a, 3) and (1, – 3) are collinear, find the value of a

Exercise 5.2 | Q 7 | Page 220

The line through the points (– 2, a) and (9, 3) has slope -1/2 Find the value of a

Exercise 5.2 | Q 8 | Page 220

The line through the points (– 2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

Exercise 5.2 | Q 9. (i) | Page 220

Show that the given points form a right angled triangle and check whether they satisfy Pythagoras theorem

A(1, – 4), B(2, – 3) and C(4, – 7)

Exercise 5.2 | Q 9. (ii) | Page 220

Show that the given points form a right angled triangle and check whether they satisfy Pythagoras theorem

L(0, 5), M(9, 12) and N(3, 14)

Exercise 5.2 | Q 10 | Page 221

Show that the given points form a parallelogram:

A(2.5, 3.5), B(10, – 4), C(2.5, – 2.5) and D(– 5, 5)

Exercise 5.2 | Q 11 | Page 221

If the points A(2, 2), B(– 2, – 3), C(1, – 3) and D(x, y) form a parallelogram then find the value of x and y

Exercise 5.2 | Q 12 | Page 221

Let A(3, – 4), B(9, – 4), C(5, – 7) and D(7, – 7). Show that ABCD is a trapezium.

Exercise 5.2 | Q 13 | Page 221

A quadrilateral has vertices at A(– 4, – 2), B(5, – 1), C(6, 5) and D(– 7, 6). Show that the mid-points of its sides form a parallelogram.

Exercise 5.3 [Pages 229 - 230]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.3 [Pages 229 - 230]

Exercise 5.3 | Q 1. (i) | Page 229

Find the equation of a straight line passing through the mid-point of a line segment joining the points (1, – 5), (4, 2) and parallel to X-axis

Exercise 5.3 | Q 1. (ii) | Page 229

Find the equation of a straight line passing through the mid-point of a line segment joining the points (1, – 5), (4, 2) and parallel to Y-axis

Exercise 5.3 | Q 2 | Page 229

The equation of a straight line is 2(x – y) + 5 = 0. Find its slope, inclination and intercept on the Y-axis

Exercise 5.3 | Q 3 | Page 229

Find the equation of a line whose inclination is 30˚ and making an intercept – 3 on the Y-axis.

Exercise 5.3 | Q 4 | Page 229

Find the slope and y intercept of sqrt(3x) + (1 - sqrt(3))y = 3

Exercise 5.3 | Q 5 | Page 229

Find the value of ‘a’, if the line through (– 2, 3) and (8, 5) is perpendicular to y = ax + 2

Exercise 5.3 | Q 6 | Page 230

The hill in the form of a right triangle has its foot at (19, 3). The inclination of the hill to the ground is 45°. Find the equation of the hill joining the foot and top.

Exercise 5.3 | Q 7. (i) | Page 230

Find the equation of a line through the given pair of point (2,2/3) and ((-1)/2, -2)

Exercise 5.3 | Q 7. (ii) | Page 230

Find the equation of a line through the given pair of point (2, 3) and (– 7, – 1)

Exercise 5.3 | Q 8 | Page 230

A cat is located at the point(– 6, – 4) in xy plane. A bottle of milk is kept at (5, 11). The cat wish to consume the milk travelling through shortest possible distance. Find the equation of the path it needs to take its milk.

Exercise 5.3 | Q 9 | Page 230

Find the equation of the median and altitude of ΔABC through A where the vertices are A(6, 2), B(– 5, – 1) and C(1, 9)

Exercise 5.3 | Q 10 | Page 230

Find the equation of a straight line which has slope (−5)/4 and passing through the point (– 1, 2).

Exercise 5.3 | Q 11. (i) | Page 230

You are downloading a song. The percent y (in decimal form) of megabytes remaining to get downloaded in x seconds is given by y = – 0.1x + 1 find the total MB of the song.

Exercise 5.3 | Q 11. (ii) | Page 230

You are downloading a song. The percent y (in decimal form) of megabytes remaining to get downloaded in x seconds is given by y = – 0.1x + 1 after how many seconds will 75% of the song gets downloaded?

Exercise 5.3 | Q 11. (iii) | Page 230

You are downloading a song. The percent y (in decimal form) of megabytes remaining to get downloaded in x seconds is given by y = – 0.1x + 1 after how many seconds the song will be downloaded completely?

Exercise 5.3 | Q 12. (i) | Page 230

Find the equation of a line whose intercepts on the x and y axes are given below

4, – 6

Exercise 5.3 | Q 12. (ii) | Page 230

Find the equation of a line whose intercepts on the x and y axes are given below

- 5, 3/4

Exercise 5.3 | Q 13. (i) | Page 230

Find the intercepts made by the following line on the coordinate axes

3x – 2y – 6 = 0

Exercise 5.3 | Q 13. (ii) | Page 230

Find the intercepts made by the following line on the coordinate axes

4x + 3y + 12 = 0

Exercise 5.3 | Q 14. (i) | Page 230

Find the equation of a straight line passing through (1, – 4) and has intercepts which are in the ratio 2 : 5

Exercise 5.3 | Q 14. (ii) | Page 230

Find the equation of a straight line passing through (– 8, 4) and making equal intercepts on the coordinate axes

Exercise 5.4 [Page 235]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.4 [Page 235]

Exercise 5.4 | Q 1. (i) | Page 235

Find the slope of the following straight line

5y – 3 = 0

Exercise 5.4 | Q 1. (ii) | Page 235

Find the slope of the following straight line

7x - 3/17 = 0

Exercise 5.4 | Q 2. (i) | Page 235

Find the slope of the line which is parallel to y = 0.7x – 11

Exercise 5.4 | Q 2. (ii) | Page 235

Find the slope of the line which is perpendicular to the line x = – 11

Exercise 5.4 | Q 3. (i) | Page 235

Check whether the given lines are parallel or perpendicular

x/3 + y/4 + 1/7 = 0 and (2x)/3 + y/2 + 1/10 = 0

Exercise 5.4 | Q 3. (ii) | Page 235

Check whether the given lines are parallel or perpendicular

5x + 23y + 14 = 0 and 23x – 5x + 9 = 0

Exercise 5.4 | Q 4 | Page 235

If the straight lines 12y = − (p + 3)x + 12, 12x – 7y = 16 are perpendicular then find ‘p’

Exercise 5.4 | Q 5 | Page 235

Find the equation of a straight line passing through the point P(−5, 2) and parallel to the line joining the points Q(3, −2) and R(−5, 4)

Exercise 5.4 | Q 6 | Page 235

Find the equation of a line passing through (6, −2) and perpendicular to the line joining the points (6, 7) and (2, −3)

Exercise 5.4 | Q 7 | Page 235

A(−3, 0) B(10, −2) and C(12, 3) are the vertices of ∆ABC. Find the equation of the altitude through A and B.

Exercise 5.4 | Q 8 | Page 235

Find the equation of the perpendicular bisector of the line joining the points A(− 4, 2) and B(6, − 4)

Exercise 5.4 | Q 9 | Page 235

Find the equation of a straight line through the intersection of lines 7x + 3y = 10, 5x – 4y = 1 and parallel to the line 13x + 5y + 12 = 0

Exercise 5.4 | Q 10 | Page 235

Find the equation of a straight line through the intersection of lines 5x – 6y = 2, 3x + 2y = 10 and perpendicular to the line 4x – 7y + 13 = 0

Exercise 5.4 | Q 11 | Page 235

Find the equation of a straight line joining the point of intersection of 3x + y + 2 = 0 and x – 2y – 4 = 0 to the point of intersection of 7x – 3y = – 12 and 2y = x + 3

Exercise 5.4 | Q 12 | Page 235

Find the equation of a straight line through the point of intersection of the lines 8x + 3y = 18, 4x + 5y = 9 and bisecting the line segment joining the points (5, −4) and (−7, 6)

Exercise 5.5 [Pages 235 - 236]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 5 Coordinate Geometry Exercise 5.5 [Pages 235 - 236]

#### Multiple choice questions

Exercise 5.5 | Q 1 | Page 235

The area of triangle formed by the points (− 5, 0), (0, – 5) and (5, 0) is

• 0 sq.units

• 25 sq.units

• 5 sq.units

• none of these

Exercise 5.5 | Q 2 | Page 235

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y-axis. The path travelled by the man is

• x = 10

• y = 10

• x = 0

• y = 0

Exercise 5.5 | Q 3 | Page 235

The straight line given by the equation x = 11 is

• parallel to X-axis

• parallel to Y-axis

• passing through the origin

• passing through the point (0, 11)

Exercise 5.5 | Q 4 | Page 236

If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

• 3

• 6

• 9

• 12

Exercise 5.5 | Q 5 | Page 236

The point of intersection of 3x – y = 4 and x + 7 = 8 is

• (5, 3)

• (2, 4)

• (3, 5)

• (4, 4)

Exercise 5.5 | Q 6 | Page 236

The slope of the line joining (12, 3), (4, a) is 1/8. The value of ‘a’ is

• 1

• 4

• − 5

• 2

Exercise 5.5 | Q 7 | Page 236

The slope of the line which is perpendicular to a line joining the points (0, 0) and (− 8, 8) is

• − 1

• 1

• 1/3

• − 8

Exercise 5.5 | Q 8 | Page 236

If slope of the line PQ is 1/sqrt(3) then slope of the perpendicular bisector of PQ is

• sqrt(3)

• -sqrt(3)

• 1/sqrt(3)

• 0

Exercise 5.5 | Q 9 | Page 236

If A is a point on the Y-axis whose ordinate is 8 and B is a point on the X-axis whose abscissae is 5 then the equation of the line AB is

• 8x + 5y = 40

• 8x – 5y = 40

• x = 8

• y = 5

Exercise 5.5 | Q 10 | Page 236

The equation of a line passing through the origin and perpendicular to the line 7x − 3y + 4 = 0 is

• 7x – 3y + 4 = 0

• 3x – 7y + 4 = 0

• 3x + 7y = 0

• 7x – 3y = 0

Exercise 5.5 | Q 11 | Page 236

Consider four straight lines
(i) l1; 3y = 4x + 5
(ii) l2; 4y = 3x – 1
(iii) l3; 4y + 3x = 7
(iv) l4; 4x + 3y = 2
Which of the following statement is true?

• l1 and l2 are perpendicular

• l2 and l4 are parallel

• l2 and l4 are perpendicular

• l2 and l3 are parallel

Exercise 5.5 | Q 12 | Page 236

A straight line has equation 8y = 4x + 21. Which of the following is true

• The slope is 0.5 and the y intercept is 2.6

• The slope is 5 and the y intercept is 1.6

• The slope is 0.5 and the y intercept is 1.6

• The slope is 5 and the y intercept is 2.6

Exercise 5.5 | Q 13 | Page 236

When proving that a quadrilateral is a trapezium, it is necessary to show

• Two sides are parallel

• Two parallel and two non-parallel sides

• Opposite sides are parallel

• All sides are of equal length

Exercise 5.5 | Q 14 | Page 236

When proving that a quadrilateral is a parallelogram by using slopes you must find

• The slopes of two sides

• The slopes of two pair of opposite sides

• The lengths of all sides

• Both the lengths and slopes of two sides

Exercise 5.5 | Q 15 | Page 236

(2, 1) is the point of intersection of two lines

• x – y – 3 = 0; 3x – y – 7 = 0

• x + y = 3; 3x + y = 7

• 3x + y = 3; x + y = 7

• x + 3y – 3 = 0; x – y – 7 = 0

Unit Exercise – 5 [Page 237]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 5 Coordinate Geometry Unit Exercise – 5 [Page 237]

Unit Exercise – 5 | Q 1 | Page 237

PQRS is a rectangle formed by joining the points P(– 1, – 1), Q(– 1, 4), R(5, 4) and S(5, – 1). A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.

Unit Exercise – 5 | Q 2 | Page 237

The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex.

Unit Exercise – 5 | Q 3 | Page 237

Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0

Unit Exercise – 5 | Q 4 | Page 237

If vertices of a quadrilateral are at A(– 5, 7), B(– 4, k), C(– 1, – 6) and D(4, 5) and its area is 72 sq. units. Find the value of k.

Unit Exercise – 5 | Q 5 | Page 237

Without using distance formula, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are vertices of a parallelogram

Unit Exercise – 5 | Q 6 | Page 237

Find the equations of the lines, whose sum and product of intercepts are 1 and – 6 respectively

Unit Exercise – 5 | Q 7 | Page 237

The owner of a milk store finds that he can sell 980 litres of milk each week at ₹ 14/litre and 1220 litres of milk each week at ₹ 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at ₹ 17/litre?

Unit Exercise – 5 | Q 8 | Page 237

Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.

Unit Exercise – 5 | Q 9 | Page 237

Find the equation of a line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

Unit Exercise – 5 | Q 10 | Page 237

A person standing at a junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 seek to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find the equation of the path that he should follow.

## Chapter 5: Coordinate Geometry

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4Exercise 5.5Unit Exercise – 5

## Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board chapter 5 - Coordinate Geometry

Samacheer Kalvi solutions for Mathematics Class 10 SSLC 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 10 SSLC 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 10 SSLC Tamil Nadu State Board chapter 5 Coordinate Geometry are Area of a Triangle by Heron's Formula, Inclination of a Line, Straight Line, General Form of a Straight Line, Coordinate Geometry, Area of a General Quadrilateral.

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