In what ratio is the line joining the points 3/4 and?

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

Let P(0 , y ) be the point of intersection of y-axis with the line segment joining A (−3,−4) and B (1,−2) which divides the line segment AB in the ratio λ : 1 .

Now according to the section formula if point a point P divides a line segment joining` A (x_1 ,y_1) " and " B (x_2 , y_2)` in the ratio m:n internally than,

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

Now we will use section formula as,

`(0 , y) = ((lambda -3)/(lambda + 1) , (-2lambda -4)/(lambda+1))`

Now equate the x component on both the sides,

`(lambda - 3 ) /(lambda +1) = 0`

On further simplification,

`lambda = 3`

So y-axis divides AB in the ratio `3/1`

Concept:

Let A = (x1 ,y1) and B = (x2 ,y2) be any two-point. let P (x,y) be any point on AB and

By section formula we have,

\(\rm x = \frac{m_2x_1+m_1x_2}{m_1+m_2}\) and \(\rm y = \frac{m_2y_1+m_1y_2}{m_1+m_2}\)