Question

if AandB are(-2, 2) and (2,-4) respectively, find the coordinates of p such that AP=3/7 AB and places on the line segment AB​

Answer 1

Answer:

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Answer 2

Answer:

-2/7, -4/7

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= 3/7 AB

Now,

AP= 3/7 AB(Given)

7AP=3(AP+BP)

7AP=3AP+3BP

⇒7AP−3AP=3BP

⇒ AP/BP = 3/4

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 (x1 ,y1) and (x2,y2 ) in the ration m:n, then coordinates of the point is given as-

(h,k)=(mx2+nx1/m+n), (my2+ny1/m+n)

Therefore,

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

(-2/7, -4/7)

Hence, the coordinates of P are ( -2/7, -4/7).