Question

25.If A and B are (-2,-2) and (2,-4) respectively, find the coordinates of P if AP = 2/7 AB and P lies on the line segment AB​

Answer 1

Answer:

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Step-by-step explanation:

Given:- A line segment joining the points A(−2,−2) and B(2,−4). P is a point on AB such that AP= 73

AB.

Now,

AP= 73

AB(Given)

7AP=3(AP+BP)

7AP=3AP+3BP

⇒7AP−3AP=3BP

⇒ BP

AP = 43

Therefore,

Point P divides AB internally in the ratio 3:4.

As we know that if a point (h,k) divides a line joining the point (x 1 ,y 1 ) and (x 2 ,y 2 ) in the ration m:n, then coordinates of the point is given as-

(h,k)=( m+nmx 2 +nx 1 , m+nmy 2+ny 1 )

Therefore,

Coordinates of P=( 3+43×(2)+4×(−2), 3+43×(−4)+4×(−2) )

=( 7−2 , 7−20 )

Hence, the coordinates of P are ( 7−2 , 7−20 )