Find the coordinates of the point of trisection of the line segment joining the points A(2,3) and B(-7,4).
Find the coordinates of the point of trisection of the line segment joining the points A(2,3) and B(-7,4).
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Step-by-step explanation:
Given:- A(2,−2) and B(−7,4)
For point of trisection, AB is divided into 3 equal parts.
Let the two trisection points are P(x,y) and Q(c,d).
Hence P divides AB in ratio 1:2 and Q divides AB in ratio 2:1.
By section formula:
x=
m+n
mx
2
+nx
1
and y=
m+n
my
2
+ny
1
x=
3
4−7
=−1 and y=
3
4−4
=0
So,P(x,y)=(−1,0).
Again by section formula:
c=
3
−14+2
=−4 and d=
3
8−2
=2
So, Q(c,d)=(−4,2).