Selina Textbook Solutions: Section and Mid-Point Formula | Mathematics Class 10 ICSE PDF Download

 Page 1


Section and Mid-Point Formula 
 
Exercise 13A 
Question 1. 
Calculate the co-ordinates of the point P which divides the line segment joining: 
(i) A (1, 3) and B (5, 9) in the ratio 1: 2. 
(ii) A (-4, 6) and B (3, -5) in the ratio 3: 2. 
 
Solution: 
 
 
Question 2. 
In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. 
 
Solution: 
Let the line joining points A (2, -3) and B (5, 6) be divided by point P (x, 0) in the ratio k: 1. 
 
Page 2


Section and Mid-Point Formula 
 
Exercise 13A 
Question 1. 
Calculate the co-ordinates of the point P which divides the line segment joining: 
(i) A (1, 3) and B (5, 9) in the ratio 1: 2. 
(ii) A (-4, 6) and B (3, -5) in the ratio 3: 2. 
 
Solution: 
 
 
Question 2. 
In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. 
 
Solution: 
Let the line joining points A (2, -3) and B (5, 6) be divided by point P (x, 0) in the ratio k: 1. 
 
 
Thus, the required ratio is 1: 2. 
Question 3. 
In what ratio is the line joining (2, -4) and (-3, 6) divided by the y-axis. 
 
Solution: 
 
Let the line joining points A (2, -4) and B (-3, 6) be divided by point P (0, y) in the ratio k:  
1. 
 
 
Thus, the required ratio is 2: 3. 
Question 4. 
In what ratio does the point (1, a) divided the join of (-1, 4) and (4, -1)? Also, find the 
value of a. 
 
Solution: 
 
 
Page 3


Section and Mid-Point Formula 
 
Exercise 13A 
Question 1. 
Calculate the co-ordinates of the point P which divides the line segment joining: 
(i) A (1, 3) and B (5, 9) in the ratio 1: 2. 
(ii) A (-4, 6) and B (3, -5) in the ratio 3: 2. 
 
Solution: 
 
 
Question 2. 
In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. 
 
Solution: 
Let the line joining points A (2, -3) and B (5, 6) be divided by point P (x, 0) in the ratio k: 1. 
 
 
Thus, the required ratio is 1: 2. 
Question 3. 
In what ratio is the line joining (2, -4) and (-3, 6) divided by the y-axis. 
 
Solution: 
 
Let the line joining points A (2, -4) and B (-3, 6) be divided by point P (0, y) in the ratio k:  
1. 
 
 
Thus, the required ratio is 2: 3. 
Question 4. 
In what ratio does the point (1, a) divided the join of (-1, 4) and (4, -1)? Also, find the 
value of a. 
 
Solution: 
 
 
 
Question 5. 
In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8)? Also, find the value 
of a. 
 
Solution: 
Let the point P (a, 6) divides the line segment joining A (-4, 3) and B (2, 8) in the ratio k: 
1. 
 
Using section formula, we have: 
 
 
Question 6. 
In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-
ordinates of the point of intersection. 
 
Page 4


Section and Mid-Point Formula 
 
Exercise 13A 
Question 1. 
Calculate the co-ordinates of the point P which divides the line segment joining: 
(i) A (1, 3) and B (5, 9) in the ratio 1: 2. 
(ii) A (-4, 6) and B (3, -5) in the ratio 3: 2. 
 
Solution: 
 
 
Question 2. 
In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. 
 
Solution: 
Let the line joining points A (2, -3) and B (5, 6) be divided by point P (x, 0) in the ratio k: 1. 
 
 
Thus, the required ratio is 1: 2. 
Question 3. 
In what ratio is the line joining (2, -4) and (-3, 6) divided by the y-axis. 
 
Solution: 
 
Let the line joining points A (2, -4) and B (-3, 6) be divided by point P (0, y) in the ratio k:  
1. 
 
 
Thus, the required ratio is 2: 3. 
Question 4. 
In what ratio does the point (1, a) divided the join of (-1, 4) and (4, -1)? Also, find the 
value of a. 
 
Solution: 
 
 
 
Question 5. 
In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8)? Also, find the value 
of a. 
 
Solution: 
Let the point P (a, 6) divides the line segment joining A (-4, 3) and B (2, 8) in the ratio k: 
1. 
 
Using section formula, we have: 
 
 
Question 6. 
In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-
ordinates of the point of intersection. 
 
Solution: 
Let the point P (x, 0) on x-axis divides the line segment joining A (4, 3) and B (2, -6) in the 
ratio k: 1. 
 
Using section formula, we have: 
 
 
Question 7. 
Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, find the 
coordinates of the point of intersection. 
 
Solution: 
 
Let S (0, y) be the point on y-axis which divides the line segment PQ in the ratio k: 1. 
Using section formula, we have: 
 
 
 
Page 5


Section and Mid-Point Formula 
 
Exercise 13A 
Question 1. 
Calculate the co-ordinates of the point P which divides the line segment joining: 
(i) A (1, 3) and B (5, 9) in the ratio 1: 2. 
(ii) A (-4, 6) and B (3, -5) in the ratio 3: 2. 
 
Solution: 
 
 
Question 2. 
In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. 
 
Solution: 
Let the line joining points A (2, -3) and B (5, 6) be divided by point P (x, 0) in the ratio k: 1. 
 
 
Thus, the required ratio is 1: 2. 
Question 3. 
In what ratio is the line joining (2, -4) and (-3, 6) divided by the y-axis. 
 
Solution: 
 
Let the line joining points A (2, -4) and B (-3, 6) be divided by point P (0, y) in the ratio k:  
1. 
 
 
Thus, the required ratio is 2: 3. 
Question 4. 
In what ratio does the point (1, a) divided the join of (-1, 4) and (4, -1)? Also, find the 
value of a. 
 
Solution: 
 
 
 
Question 5. 
In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8)? Also, find the value 
of a. 
 
Solution: 
Let the point P (a, 6) divides the line segment joining A (-4, 3) and B (2, 8) in the ratio k: 
1. 
 
Using section formula, we have: 
 
 
Question 6. 
In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-
ordinates of the point of intersection. 
 
Solution: 
Let the point P (x, 0) on x-axis divides the line segment joining A (4, 3) and B (2, -6) in the 
ratio k: 1. 
 
Using section formula, we have: 
 
 
Question 7. 
Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, find the 
coordinates of the point of intersection. 
 
Solution: 
 
Let S (0, y) be the point on y-axis which divides the line segment PQ in the ratio k: 1. 
Using section formula, we have: 
 
 
 
 
Question 8. 
Points A, B, C and D divide the line segment joining the point (5, -10) and the origin in 
five equal parts. Find the co-ordinates of A, B, C and D. 
 
Solution: