d(A,B) =10 d(B,C) =15 and d(A,C) = 5 Are the points A,B,C collinear ? If yes give betweenness relation
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Answer:
Correct option is
A
(1, 6)
If three points P(x
1
,y
1
),Q,R(x
2
,y
2
) are collinear.
⇒PQ=QR and Q is the midpoint of PR
The mid point Q=(
2
x
1
+x
2
,
2
y
1
+y
2
)
Given, the points A(5,2),B(3,4) and C(x,y) are collinear and AB=BC
⇒ B is the mid-point of AC.
Using midpoint formula,
(
2
x+5
,
2
y+2
)=(3,4)
⟹
2
x+5
=3 and
2
y+2
=4
⟹x+5=6 and y+2=8
⟹x=1 and y=6
Hence, the coordinates of C are (1,6).
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