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Mathematics

The line segment joining A(-7, 2) and B(3, -8) is divided by the x-axis in the ratio :

  1. 1 : 4

  2. 3 : 7

  3. 4 : 1

  4. 7 : 3

Straight Line Eq

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Answer

Given,

AB is divided by the x-axis, thus y-coordinate = 0 at point of division.

A(-7, 2) and B(3, -8)

Let ratio be m : n.

By section-formula,

y = my2+ny1m+n\dfrac{my2 + ny1}{m + n}

Substituting values we get :

⇒ 0 = m×(−8)+n×(2)m+n\dfrac{m \times (-8) + n \times (2)}{m + n}

⇒ 0 = -8m + 2n

⇒ 8m = 2n

⇒ mn=28\dfrac{m}{n} = \dfrac{2}{8}

⇒ mn=14\dfrac{m}{n} = \dfrac{1}{4}

⇒ m : n = 1 : 4.

Hence, option 1 is the correct option.

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