Find the coordinates of the points of trisection (i.e., points dividing into three equal parts) of the line segment joining the points A(2, – 2) and B(– 7, 4).
Answers
Answer:
Given:- A line segment joining the points A(2,−2) and B(−7,4).
Let P and Q be the points on AB such that,
AP=PQ=QB
Therefore,
P and Q divides AB internally in the ratio 1:2 and 2:1 respectively.
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=(
1+2
1×(−7)+2×2
,
1+2
1×4+2×(−2)
)=(−1,0)
Coordinates of Q=(
1+2
2×(−7)+1×2
,
1+2
2×4+1×(−2)
)=(−4,2)
Therefore, the coordinates of the points of trisection of the line segment joining A and B are (−1,0) and (−4,2).
Step-by-step explanation:
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Step-by-step explanation:
Answer:
Given:- A line segment joining the points A(2,−2) and B(−7,4).
Let P and Q be the points on AB such that,
AP=PQ=QB
Therefore,
P and Q divides AB internally in the ratio 1:2 and 2:1 respectively.
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=(
1+2
1×(−7)+2×2
,
1+2
1×4+2×(−2)
)=(−1,0)
Coordinates of Q=(
1+2
2×(−7)+1×2
,
1+2
2×4+1×(−2)
)=(−4,2)
Therefore, the coordinates of the points of trisection of the line segment joining A and B are (−1,0) and (−4,2).
Step-by-step explanation:
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