find the co ordinates of the point of trisection of the line segment joining the joint A(-10,7) and B(4,2)
Answers
Explanation:
trisection of the line segment joining (4,−1) and (−2,−3).
Medium
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Answer
Given coordinates are(x
1
,y
1
)=(4,−1)
and (x
2
,y
2
)=(−2,−3)
Means of trisection:- A line segment in three equal parts then ratio is 1:2 and 2:1 internally.
Case (1) If m
1
:m
2
=1:2
Then, using formula
(x,y)=(
m
1
+m
2
m
1
x
2
+m
2
x
1
,
m
1
+m
2
m
1
y
2
+m
2
y
1
)
(x,y)=(
1+2
1×(−2)+2×4
,
1+2
1×(−3)+2×(−1)
)
(x,y)=(
3
−2+8
,
3
−3−2
)
(x,y)=(2,−
3
5
)
Case (2):-
If m
1
:m
2
=2:1
Then, using formula
(x,y)=(
m
1
+m
2
m
1
x
2
+m
2
x
1
,
m
1
+m
2
m
1
y
2
+m
2
y
1
)
(x,y)=(
2+1
2×(−2)+1×4
,
1+2
2×(−3)+1×(−1)
)
(x,y)=(
3
−4+4
,
3
−6−1
)
(x,y)=(0,−
3
7
)
Hence, this is the answer.
HOPE IT HELPS YOU...
GOOD EVENING...
Answer:
We know that trisection divides the line segment in the ratio 1:2 or 2:1 internally. Let the line segment be PQ. Let A (x, y) divides the line segment PQ in the ratio 1:2. Now by using the section formula let us find the A (x, y) coordinates, where the ratio m: n=1:2 and point are P (-3, 4) and Q (4, 5).
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