Let P and Q be the points of trisection of the line segment joining the points A(2, – 2) and B(–7, 4) such that P is nearer to A. The coordinates of P and Q are given by
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Let P and Q be the points of trisection of the line segment joining the points A(2,−2) and B(−7,4) such that P is nearer to A. Find the coordinates of P and Q.
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Since P and Q be the points of trisection of the line segment joining the points A(2,−2) and B(−7,4) such that P is nearer to A.
Therefore, P divides line segment in the ratio 1:2 and Q divides in 2:1 as shown in the figure.
Using section formula,
Coordinates of P = [
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
]
= [
1+2
1(−7)+2(2)
,
1+2
1(4)+2(−2)
]
= [
3
−3
,
3
0
]
= [−1,0]
Coordinates of Q =[
2+1
2(−7)+1(2)
,
2+1
2(4)−1(−2)
]
= [
3
−12
,
3
6
]
= [−4,2]