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The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the
a. I quadrant
b. II quadrant
c. III quadrant
d. IV quadrant

Solution:

We know that

The coordinates of the point P which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁: m₂ are

\([\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}]\)

It is given that

(x₁, y₁) = (7, -6)

(x₂, y₂) = (3, 4)

m₁ = 1

m₂ = 2

Substituting the values in the section formula

= \([\frac{1\times 3+2\times 7}{1+2},\frac{1\times 4+2\times -6}{1+2}]=(\frac{17}{3},\frac{-8}{3})\)

As the x coordinate is positive and y coordinate is negative

The point lies in the IV quadrant.

Therefore, the points (7, -6) and (3, 4) in ratio 1 : 2 internally lie in the IV quadrant.

✦ Try This: The point which divides the line segment joining the points (6, -4) and (2, 6) in ratio 1 : 4 internally lies in the

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.1 Problem 9

The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the a. I quadrant, b. II quadrant, c. III quadrant, d. IV quadrant

Summary:

The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the IV quadrant

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