Question

IfA and B are (-2, -2) and (2, -4) respectively. Find the coordinates of p such that AP=3/7AB and p lines on the segment AB​

Answer 1

Answer:

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

7

3

AB.

Now,

AP=

7

3

AB(Given)

7AP=3(AP+BP)

7AP=3AP+3BP

⇒7AP−3AP=3BP

⇒

BP

AP

=

4

3

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+n

mx

2

+nx

1

m+n

my

2

+ny

1

Therefore,

Coordinates of P=(

3+4

3×(2)+4×(−2

3+4

3×(−4)+4×(−2)

7

−2

7

−20

Hence, the coordinates of P are (

7

−2

7

−20

Answer 2

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