If the coordinates of points A and B are (-2,-2) and (2, -4) respectively, what are the coordinates of P such that AP AB, where P lies on the line segment AB? A 2. 7 ? -20 7 B (, 20) С - 20 - 2 7 9 7 D (20,4)
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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
).
Step-by-step explanation:
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