Question

8. If A and B are (-2, - 2) and (2, - 4), respectively, find the coordinates of P such that

AP=3/7
AB and Plies on the line segment AB.
​

Answer 1

Answer:

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=  

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

​  

).