4. Find the ratio in which (-3, 9) divides the line segment joining the
points (-5,-4) and (-2, 3). Find the value of q.

October 15, 2021

By Caroline

1 thought on “4. Find the ratio in which (-3, 9) divides the line segment joining the<br /> points (-5,-4) and (-2, 3). Find the value of q.<br”

1. Step-by-step explanation:

   Using the section formula, if a point (x,y) divides the line joining the points (x

   1

   ,y

   1

   ) and (x

   2

   ,y

   2

   ) in the ratio m

   1

   :m

   2

   , then

   (x,y)=(

   m

   1

   +m

   2

   m

   1

   x

   2

   +m

   2

   x

   1

   ,

   m

   1

   +m

   2

   m

   1

   y

   2

   +m

   2

   y

   1

   )

   Given that ratio m

   1

   :m

   2

   =xy

   points A(−5,−4) and B(−2,3)

   Let ratio be

   m

   2

   m

   1

   =

   1

   m

   Therefore,

   x=

   m

   1

   +m

   2

   m

   1

   x

   2

   +m

   2

   x

   1

   −3=

   m+1

   m.(−2)+(1)(−5)

   −3(m+1)=−2m−5

   −3m−3=−2m−5

   −3+5=−2m+3m

   m=2

   m

   2

   m

   1

   =

   1

   2

   Now, k=

   m

   1

   +m

   2

   m

   1

   .y

   2

   +m

   2

   .y

   1

   k=

   2+1

   2.(3)+1(−4)

   k=

   3

   6−4

   k=2/3

   ∴k=2/3

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