Mid point formula class 10

Selina Solutions Concise Maths Class 10 Chapter 13 Section and Mid-Point Formula For any two given points in a Cartesian plane, the knowledge of co-ordinate geometry is essential to find: (i) the distance between the given points, (ii) the co-ordinates of a point which divides the line joining the given points in a given ratio and (iii) the co-ordinates of the mid-point of the line segment joining the two given points. Students in this chapter will solve problems on the section formula, points of trisection, mid-point formula and centroid of a triangle. The Exercises of Concise Selina Solutions Class 10 Maths Chapter 13 Section and Mid-Point Formula Access Selina Solutions Concise Maths Class 10 Chapter 13 Section and Mid-Point Formula Exercise 13(A) Page No: 177 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: (i) Let’s assume the co-ordinates of the point P be (x, y) Then by section formula, we have P(x, y) = (m 1x 2 + m 2x 1)/ (m 1 + m 2), (m 1y 2 + m 2y 1)/ (m 1 + m 2) Hence, the co-ordinates of point P are (7/3, 5). (ii) Let’s assume the co-ordinates of the point P be (x, y) Then by section formula, we have P(x, y) = (m 1x 2 + m 2x 1)/ (m 1 + m 2), (m 1y 2 + m 2y 1)/ (m 1 + m 2) Hence, the co-ordinates of point P are (1/5, -3/5). 2. In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. Solution: Let’s as...

• Your answer should be • an integer, like 6 6 6 6 • a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5 • a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4 • a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4 • an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75 • a multiple of pi, like 12 pi 12\ \text 2 / 3 pi 2, slash, 3, space, start text, p, i, end text units

Exercise 13(A) 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 (i) Let’s assume the co-ordinates of the point P be (x, y) Then by section formula, we have P(x, y) = (m 1x 2+ m 2x 1)/ (m 1+ m 2), (m 1y 2+ m 2y 1)/ (m 1+ m 2) Hence, the co-ordinates of point P are (1/5, -3/5). 2. In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. Solution Let’s assume the joining points as A(2, -3) and B(5, 6) be divided by point P(x ,0) in the ratio k: 1. Then we have, y = ky 2+ y 1/ (k + 1) ⇒ 0 = 6k + (-3)/(k + 1) ⇒ 0 = 6k – 3 ⇒ k = ½ Hence, the required ratio is 1: 2. 3. In what ratio is the line joining (2, -4) and (-3, 6) divided by the y-axis. Solution Let’s assume the line joining points A(2, -4) and B(-3, 6) be divided by point P (0, y) in the ratio k: 1. Then we have, x = kx 2+ x 1/ (k + 1) ⇒ 0 = k(-3) + (1×2)/ (k + 1) ⇒ 0 = -3k + 2 ⇒ k = 2/3 Hence, the required ratio is 2: 3. 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 Let’s assume the point P (1, a) divide the line segment AB in the ratio k: 1. Then by section formula, we have 1 = (4k – 1)/ (k + 1), ⇒ k + 1 = 4k – 1 ⇒ 2 = 3k ⇒ k = 2/3 ….. (1) And, a = (-k + 4)/ (k + 1) ⇒ a = (-(2/3) + 4)/(2/3 + 1) [using (1)] ⇒ a = 10/5 = 2 Thus, the required ratio is 2: 3 and a = 2. 5. In what ratio does the point ...

The midpoint \blueD) ( x 2 ​ , y 2 ​ ) left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis is given by the following formula: ( x 1 + x 2 2 , y 1 + y 2 2 ) \left(\greenD\right) ( 2 x 1 ​ + x 2 ​ ​ , 2 y 1 ​ + y 2 ​ ​ ) left parenthesis, start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54, comma, start color #e07d10, start fraction, y, start subscript, 1, end subscript, plus, y, start subscript, 2, end subscript, divided by, 2, end fraction, end color #e07d10, right parenthesis Let's start by plotting the points ( x 1 , y 1 ) (\greenD) ( x 2 ​ , y 2 ​ ) left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis . An expression for the x x x x -coordinate of the midpoint \blueD 2 x 1 ​ + x 2 ​ ​ start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54 : The first quadrant of a coordinate plane with two tick marks on the x axis labeled x one and x two. There are two tick marks on the y axis labeled y one and y two. There is a point at x one, y one and another point at x two, ...

• Your answer should be • an integer, like 6 6 6 6 • a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5 • a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4 • a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4 • an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75 • a multiple of pi, like 12 pi 12\ \text 2 / 3 pi 2, slash, 3, space, start text, p, i, end text units

Selina Solutions Concise Maths Class 10 Chapter 13 Section and Mid-Point Formula For any two given points in a Cartesian plane, the knowledge of co-ordinate geometry is essential to find: (i) the distance between the given points, (ii) the co-ordinates of a point which divides the line joining the given points in a given ratio and (iii) the co-ordinates of the mid-point of the line segment joining the two given points. Students in this chapter will solve problems on the section formula, points of trisection, mid-point formula and centroid of a triangle. The Exercises of Concise Selina Solutions Class 10 Maths Chapter 13 Section and Mid-Point Formula Access Selina Solutions Concise Maths Class 10 Chapter 13 Section and Mid-Point Formula Exercise 13(A) Page No: 177 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: (i) Let’s assume the co-ordinates of the point P be (x, y) Then by section formula, we have P(x, y) = (m 1x 2 + m 2x 1)/ (m 1 + m 2), (m 1y 2 + m 2y 1)/ (m 1 + m 2) Hence, the co-ordinates of point P are (7/3, 5). (ii) Let’s assume the co-ordinates of the point P be (x, y) Then by section formula, we have P(x, y) = (m 1x 2 + m 2x 1)/ (m 1 + m 2), (m 1y 2 + m 2y 1)/ (m 1 + m 2) Hence, the co-ordinates of point P are (1/5, -3/5). 2. In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. Solution: Let’s as...

The midpoint \blueD) ( x 2 ​ , y 2 ​ ) left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis is given by the following formula: ( x 1 + x 2 2 , y 1 + y 2 2 ) \left(\greenD\right) ( 2 x 1 ​ + x 2 ​ ​ , 2 y 1 ​ + y 2 ​ ​ ) left parenthesis, start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54, comma, start color #e07d10, start fraction, y, start subscript, 1, end subscript, plus, y, start subscript, 2, end subscript, divided by, 2, end fraction, end color #e07d10, right parenthesis Let's start by plotting the points ( x 1 , y 1 ) (\greenD) ( x 2 ​ , y 2 ​ ) left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis . An expression for the x x x x -coordinate of the midpoint \blueD 2 x 1 ​ + x 2 ​ ​ start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54 : The first quadrant of a coordinate plane with two tick marks on the x axis labeled x one and x two. There are two tick marks on the y axis labeled y one and y two. There is a point at x one, y one and another point at x two, ...

Exercise 13(A) 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 (i) Let’s assume the co-ordinates of the point P be (x, y) Then by section formula, we have P(x, y) = (m 1x 2+ m 2x 1)/ (m 1+ m 2), (m 1y 2+ m 2y 1)/ (m 1+ m 2) Hence, the co-ordinates of point P are (1/5, -3/5). 2. In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis. Solution Let’s assume the joining points as A(2, -3) and B(5, 6) be divided by point P(x ,0) in the ratio k: 1. Then we have, y = ky 2+ y 1/ (k + 1) ⇒ 0 = 6k + (-3)/(k + 1) ⇒ 0 = 6k – 3 ⇒ k = ½ Hence, the required ratio is 1: 2. 3. In what ratio is the line joining (2, -4) and (-3, 6) divided by the y-axis. Solution Let’s assume the line joining points A(2, -4) and B(-3, 6) be divided by point P (0, y) in the ratio k: 1. Then we have, x = kx 2+ x 1/ (k + 1) ⇒ 0 = k(-3) + (1×2)/ (k + 1) ⇒ 0 = -3k + 2 ⇒ k = 2/3 Hence, the required ratio is 2: 3. 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 Let’s assume the point P (1, a) divide the line segment AB in the ratio k: 1. Then by section formula, we have 1 = (4k – 1)/ (k + 1), ⇒ k + 1 = 4k – 1 ⇒ 2 = 3k ⇒ k = 2/3 ….. (1) And, a = (-k + 4)/ (k + 1) ⇒ a = (-(2/3) + 4)/(2/3 + 1) [using (1)] ⇒ a = 10/5 = 2 Thus, the required ratio is 2: 3 and a = 2. 5. In what ratio does the point ...