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The Ratio in Which the Line Segment Joining Points a (A1, B1) and B (A2, B2) is Divided by Y-axis is - Mathematics

MCQ

The ratio in which the line segment joining points A (a1b1) and B (a2b2) is divided by y-axis is

Options

  • a1 : a2

  •  a1 a2

  • b1 : b2

  •  −b1 : b2

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Solution

Let P( 0 ,y)   be the point of intersection of y-axis with the line segment joining` A(a_1 , b_1) " and B " (a_2 , b_2)` which divides the line segment AB in the ratio λ : 1 .

Now according to the section formula if point a point P divides a line segment joining `A(x_1 ,y_1)  " and" B (x_2 , y_2)`  in the ratio m:n internally than,
`P ( x, y) = ((nx_1 + mx_2)/(m+n) , (ny_1 +my_2)/(m + n))`

Now we will use section formula as,

`( 0, y) = ((λa_2 +a_1)/(λ + 1) , ( λb_2 + b_1) /(λ + 1))`

Now equate the x component on both the sides,

`(λa_2 + a_1) /(λ + 1) = 0`

On further simplification,

`λ = - a_1/a_2`

 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Q 39 | Page 65
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