If PQ are the point of trisection of A (1,-2), B (-5,6), then PQ = ?
Answers
Given :
Two points A(1,-2) and B (-5,6)
Two points P & Q trisects the line AB
To Find :
Coordinates of points P & Q
Solution :
•let coordinates of P is (a,b) & coordinates of Q is (c ,d)
•By section formula, Coordinates of point which divides the line segment in ratio m1/m2 are given by
x = [ m1x2 + m2x1]/(m1+m2)
y = [ m1x2 + m2x1]/(m1+m2)
•P and Q trisects AB
AP = PQ = QB
•So, it can be said that point P divides the line AB in the ratio 1:2
a = [(1)(-5) + (2)(1)]/(1+2)
a = (-5+2)/3
a = -3/3
a = -1
b = [(1)(6) + (2)(-2)]/(1+2)
b = [ 6 - 4 ]/3
b = 2/3
Coordinates of point P are ( -1 , 2/3 )
•Also, it can be said that point Q divides the line AB in the ratio 2:1
a = [(2)(-5) + (1)(1)]/(1+2)
a = (-10+1)/3
a = -9/3
a = -3
b = [(2)(6) + (1)(-2)]/(1+2)
b = [ 12 - 2 ]/3
b = 10/3
Coordinates of point P are
( -3 , 10/3 )
Answer:
Step-by-step explanation:By section formula, Coordinates of point which divides the line segment in ratio m1/m2 are given by
x = [ m1x2 + m2x1]/(m1+m2)
y = [ m1x2 + m2x1]/(m1+m2)
•P and Q trisects AB
AP = PQ = QB
•So, it can be said that point P divides the line AB in the ratio 1:2
a = [(1)(-5) + (2)(1)]/(1+2)
a = (-5+2)/3
a = -3/3
a = -1
b = [(1)(6) + (2)(-2)]/(1+2)
b = [ 6 - 4 ]/3
b = 2/3
Coordinates of point P are ( -1 , 2/3 )
•Also, it can be said that point Q divides the line AB in the ratio 2:1
a = [(2)(-5) + (1)(1)]/(1+2)
a = (-10+1)/3
a = -9/3
a = -3
b = [(2)(6) + (1)(-2)]/(1+2)
b = [ 12 - 2 ]/3
b = 10/3
Coordinates of point P are
( -3 , 10/3
3 PQ=10