find the coordinates of the points of trisection of the line segment joining the points A(2,-2) and B(-7,4)
Answers
Answer:
Explanation:
Let the given points be A(2,−2) & B(−7,4)
P & Q are two points on AB such that
AP=PQ=QB
Let k=AP=PQ=QB
Hence comparing AP & PB
AP=k
PB=PQ+QB
=k+k=2k
Hence, ratio of AP & PB =
2m
m
=
2
1
Thus P divides AB in the ratio 1:2
Now, we have to find P
Let P be (x,y)
Hence,
m
1
=1, m
2
=2
And for AB
x
1
=2, x
2
=−2
y
1
=−7, y
2
=4
x=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
1×(−7)+2×2
=
3
−7+4
=−1
y=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
1×4+2×(−2)
=
3
4−4
=0
Hence, point P is P(−1,0)
Similarly, Point A divides AB in the ratio AQ & QB
=
QB
AQ
=
QB
AP+PQ
=
k
k+k
=
1
2
=2:1
Now, we have to find Q
Let Q be (x,y)
Hence,
m
1
=2, m
2
=1
x
1
=2, x
2
=−2
y
1
=−7, y
2
=4
x=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
2×(−7)+1×2
=
3
−14+2
=−4
y=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
2×4+1×(−2)
=
3
8−2
=2
Hence, point Q is Q(−4,2)