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Mathematics

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

  1. Ist quadrant

  2. IInd quadrant

  3. IIIrd quadrant

  4. IVth quadrant

Section Formula

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Answer

Let P(x, y) be the point which divides the line segment joining the points.

Given, A(7, -6) and B(3, 4) is divided by P in ratio 1 : 2.

By section formula,

x=m1x2+m2x1m1+m2 and y=m1y2+m2y1m1+m2=1×3+2×71+2 and 1×4+2×(6)1+2=3+143 and 4123=173 and 83.x = \dfrac{m1x2 + m2x1}{m1 + m2} \text{ and } y = \dfrac{m1y2 + m2y1}{m1 + m2} \\[1em] = \dfrac{1 \times 3 + 2 \times 7}{1 + 2} \text{ and } \dfrac{1 \times 4 + 2 \times (-6)}{1 + 2} \\[1em] = \dfrac{3 + 14}{3} \text{ and } \dfrac{4 - 12}{3} \\[1em] = \dfrac{17}{3} \text{ and } -\dfrac{8}{3}.

We see that x is positive and y is negative.

∴ It lies in the fourth quadrant.

Hence, Option 4 is the correct option.

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