1.

Find The Ratio In Which the point P(2,1) divide the line joining the points A(2,7) and B(2,-3).​

Answer»

\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}

GiveN:

  • The points are A(2,7) and B(2,-3).
  • The point which divides them is P(2,1)

To Find:

  • The ratio in which P divides AB?

Step-by-step Explanation:

Let the ratio be k:1

Hence, m1 = k and M2 = 1

Also, if we see the points:

  • x1 = 2 and y1 = 7
  • x2 = 2 and y2 = -3
  • x = 2 and y = 1

Using Section formula,

\cdot{ \boxed{ \rm{x = \frac{m1x2 + m2x1}{m1 + m2} \:}} \boxed{ \rm{ \: y = \frac{m1y2 + m2y1}{m1 + m2} }}}

Putting the given values,

\rm{1 = \dfrac{k( - 3) + 1(7)}{k + 1} }

Cross MULTIPLYING,

⇒ k + 1 = -3k + 7

⇒ k + 3k = 6

⇒ 4k = 6

⇒ k = 3/2

The ratio is k : 1

⇒ 3/2 : 1

⇒ 3 : 2

Hence, the ratio is 3 : 2 (Ans)


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