if A and B are (-2,-2) and (2,-4), respectively , find the coordinates of P such that AP=3/7 AB and P lies on the line segment AB About the author Sadie
Answer: the coordinates of P are ( 7 −2 , 7 −20 ). Step-by-step solution: 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 ). Reply
-4/5, -13/5 Step-by-step explanation: AP/AB=3/7=m/n so from section formula x=mx1+nx2/m+n=-4/5 similarly y co ordinate can be found you=my1+ny2/m+n=-13/5 here taken that A coordinates are x1, y1 and B as x2, y2 Reply
Answer:
the coordinates of P are (
7
−2
,
7
−20
).
Step-by-step solution:
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
).
-4/5, -13/5
Step-by-step explanation:
AP/AB=3/7=m/n so from section formula x=mx1+nx2/m+n=-4/5 similarly y co ordinate can be found you=my1+ny2/m+n=-13/5 here taken that A coordinates are x1, y1 and B as x2, y2