Question

Line segment AB has endpoints A(–4, –10) and B(–11, –7). To find the x-coordinate of the point that divides the directed line segment in a 3:4 ratio, the formula x = (x2 – x1) + x1 was used to find that x = (–11 – (–4)) + (–4).

Answer 1

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Answer 2

Concept

Section formula in coordinate geometry is used to find the ratio in which the line segment is divided by a point internally or externally.

Given

Line segment AB has endpoints A(–4, –10) and B(–11, –7).

Line segment AB is divided in ratio 3 : 4

Find

The coordinate of point

Solution

Let Point C( x, y ) divides the line segment AB in ratio 3 : 4.

Section formula

x = ( mx₂ + nx₁ )/( m + n )

y = ( my₂ + ny₁ )/( m + n )

Here m = 3 and n = 4

( x₁, y₁ ) = (–4, –10)

( x₂, y₂ ) = (–11, –7)

Using Section formula

x = [ 3( -11 ) + 4( -4 )] /( 3+4 )

x = [ 3( -11 ) + 4( -4 )] / 7

x = ( -33-16 )7

x = -49/7

x = -7

The x coordinate of the point which divides the line segment AB in ratio 3 : 4 is -7.

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