11.The vertices of a triangle ABC are A (1,2) , B(4,6) and C(6,14) . AD is the bisector of the angle A and meets BC at D. Find the co-ordinates of the point D. in Show that the points (3,-2),(4,0),(6,-3) and (5,- 5) are the vertices of a parallelogram.
nrn the extremities of a diagonal of a parallelogram. If
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Answer:
Step-by-step explanation:
Given the three coordinates,
A(2,1) , B(6,-2) ,C(8,9)
AB=
(−2−1)
2
+(6−2)
2
=5
AC=
(9−1)
2
+(8−2)
2
=10
By using angle bisector theorem ,
AC
AB
=
CD
BD
∴
CD
BD
=
2
1
=
n
m
By using section formula,
B=(6,−2)=(x
1
,y
1
)andC(8,9)=(x
2
,y
2
)
m=1andn=2
D=[
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
]
=(
1+2
8+12
,
1+2
9−4
)=(
3
20
,
3
5
)
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