NCERT Class 10 maths exercise 7.4 Question no.1

Chapter 7- Co-ordinate geometry

Class 10 Exercise 7.4 -Q1.Determine the ratio in which the line 2x + y – 4 = 0, divides the line segment joining the points A(2,-2) and B(3,7).

Ans.

Let the point of intersection of the given line 2x + y – 4 = 0 and the line segment joining the points A(2,-2) and B(3,7) is (x,y).

Let the point of intersection C(x,y) of line with the line segment AB divides the line segment AB in the ratio of m : n

Applying the section formula

Where k = m : n

We are given the A(2,-2) =(x₁,y₁) and B(3,7) = (x₂,y₂)

Putting the value x₁=2, x₂= 3,  y₁= -2, y₂=7

Since the point C(x,y)  lies in the line 2x + y – 4 = 0, so its co-ordinates (x,y) must satisfy the equation of line.

Therefore putting the value of     

In the given equation 2x + y – 4 = 0, we have

Therefore the ratio by which the line divides the line segment is 2 : 9

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Other related questions

Q1. Determine the coordinates of the point of intersection of a line 2x + y – 4 = 0 and the line segment joining the points (2,-2)  and (3,7) divides the line segment into 2: 9.

Q2.In which ratio the line 3x + 2y -k+3 = 0, divides the line segment joining the points (3,5) and (-3,-4) if the line is passing through the origin.

Q3.If a line 2x +3 = y is passing through ( 2, a) , find the ratio the line divides the line segment joining the points (5,-2) and (3,4).

Q4.Find the ratio in which the line segment joining the points (-3,10) and (6,-8) divided by (-1,6).

Q5.Find the ratio in which the line segment joining the points (1,-5) and (-4,5) divided by the x-axis. Also, find the coordinates of the point of division.

Q6.Find the ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4). Also, find the point of intersection.

Q7.In what ratio does the point (-4,6) divides the line segment joining the points A(-6,10) and B(3,-8).

Q8.Find the coordinates of the point which divides the line segment joining the points (4,-3) and (8,5) in the ratio 3: 1 internally.

 

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