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If the Coordinates of Points a and B Are (-2, -2) and (2, -4) Respectively. Find The Coordinates of the Point P Such that Ap= `3/7` Ab, Where P Lies on the Segment Ab. - Mathematics

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If the coordinates of points A and B are (-2, -2) and (2, -4) respectively. Find the  coordinates of the point P such that AP= `3/7`
AB, where P lies on the segment AB.

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Solution

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively.  AP= `3/7` AB,  and P lies on the  line segment AB. so

AP +BP =AB 

`⇒AP +BP = (7AP)/3                      ∵ AP = 3/7 AB`

`⇒ BP = (7AP)/3-AP`

`⇒(AP)/(BP)= 3/4`

Let (x, y) be the coordinates of P which divides AB in the ratio 3 : 4 internally Then

` x= (3 xx 2 + 4 xx(-2))/(3+4) = (6-8)/7 = - 2/7`

`y = (3xx(-4) +4 xx(-2))/(3+4) = (-12-8) /7 = -20/7`

Hence, the coordinates of point P are` (-2/7 , -20/7)`

Concept: Coordinate Geometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 3

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