In what ratio does the point 4 6 divide the line segment joining the points a 6 10 and b 3 8 prime

The co-ordinates of a point which divided two points `(x_1,y_1)` and `(x_2, x_2)` internally in the ratio m:n is given by the formula,

`(x,y) = (((mx_2 + nx_1)/(m + n))","((my_2 + ny_1)/(m + n)))`

Here it is said that the point (−4,6) divides the points A(−6,10) and B(3,−8). Substituting these values in the above formula we have,

`(-4, 6) = (((m(3) + n(-6))/(m + n))"," ((m(-8) + n(10))/
(m + n)))`

Equating the individual components we have,

`-4 = (m(3) + n(-6))/(m + n)`

-4m - 4n = 3m - 6n

7m = 2n

`m/n = 2/7`

Therefore the ratio in which the line is divided is 2 : 7

Solution:

The coordinates of the point P(x, y) which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂), internally, in the ratio m₁: m₂ is given by the Section Formula: P(x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n]

Let the ratio in which the line segment joining A(- 3, 10) and B(6, - 8) be divided by point C(- 1, 6) be k : 1.

By Section formula, C(x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n]

m = k, n = 1

Therefore,

- 1 = (6k - 3) / (k + 1)

- k - 1 = 6k - 3

7k = 2

k = 2 / 7

Hence, the point C divides line segment AB in the ratio 2 : 7.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 7

Video Solution:

NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.2 Question 4

Summary:

The ratio in which the line segment joining the points (- 3, 10) and (6, - 8) is divided by (- 1, 6) is 2 : 7.

☛ Related Questions:

Find the ratio in which the line segment joining A (1, - 5) and B (- 4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4).
If A and B are (- 2, - 2) and (2, - 4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.

Math worksheets and
visual curriculum

Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

Let P, Q and R be the three points which divide the line-segment joining the points A(-2, 2) and B(2, 8) in four equal parts.

Case I. For point P, we have

Hence, m1 = 1, m2 = 3
x1 = -2, y2 = 2
x2 = 2, y2 = 8Then, coordinates of P are given by

Case II. For point Q, we have

m1 = 2, m2 = 2
x1 = -2, y1 = 2
and x2 = 2, y2 = 8Then, coordinates of Q are given by

Case III. For point R, we have

Hence, m1 = 3, m2 = 1
x1 = -2, y1 = 2
and x2 = 2, y2 = 8Then co-ordinates of R are given by

Last updated at Aug. 16, 2021 by

Solve all your doubts with Teachoo Black (new monthly pack available now!)

Example 7 In what ratio does the point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8)? Given points A(−6, 10) & B(3, −8) Let point C(−4, 6) We need to find ratio between AC & CB Let the ratio be k : 1 Hence, m1 = k , m2 = 1 Also, x1 = −6 , y1 = 10 x2 = 3 , y2 = −8 & x = −4 , y = 6 Using section formula x = (𝑚1 𝑥2 + 𝑚2 𝑥1)/(𝑚1 + 𝑚2) −4 = (𝑘 ×3 + 1 ×−6)/(𝑘 + 1) −4 = (3𝑘 − 6)/(𝑘 + 1) −4(k + 1)= 3k − 6 −4k – 4 = 3k – 6 −4k – 3k = −6 + 4 −7k = −2 k = (−2)/(−7) k = 2/7 Hence, the ratio is k : 1 = 2/7 : 1 Multiplying 7 both sides = 7 × 2/7 : 7 × 1 = 2 : 7 So, the ratio is 2: 7