a=-1 and b=-2 and c=x3
Answers
Answer:
Answer
Correct option is
D
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
The points A(x
1
,y
1
),B(x
2
,y
2
) and C(x
3
y
3
) are the vertices of ΔABC.
∴ the median BE from B will meet AC at E which is the mid point of AC.
So, by section formula for mid point, the co-ordinates of E is E(
2
x
1
+x
3
,
2
y
1
+y
3
)=(x
4
,y
4
) .
∴ the co-ordinates of Q(x,y) are by the section formula,
x=
m+n
mx
1
+nx
4
=
2+1
2
x
1
+x
3
×2+x
2
×1
=
3
x
1
+x
2
+x
3
and y=
m+n
my
1
+ny
4
=
2+1
2
y
1
+y
3
×2+y
2
×1
=
3
y
1
+y
2
+y
3
∴Q(x,y)=(
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
).
Proceeding in the same way the co-ordinates of R(p,q), which divides the median CF in the ratio 2:1, are
p=
2+1
2
x
1
+x
2
×2+x
3
×1
=
3
x
1
+x
2
+x
3
and
q=
2+1
2
y
1
+y
2
×2+y
3
×1
=
3
y
1
+y
2
+y
3
∴R(p,q)=(
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
)
So, Q and R are same points.
Q(x,y)=R(p,q)=(
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
)
Step-by-step explanation:
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