Question

Point p trisects the line segment joining the points (5, 7) and (2, 4) then its distance from origin may be equal to :

Answer 1

The answer is $2\sqrt{13}$

P either divides the line segment in ratio 2:1 or 1:2 (as it is trisecting)

So, P=(3,5) or (4,6)

OP=$\sqrt{34}$ or $2\sqrt{13}$

Answer 2

Answer:

Distance from origin = (4,6)

Step-by-step explanation:

Point P trisects that means it divides the line in the ratio 1:2 or 2:1

Suppose a line AB is trisected by point P

A(5,7) B(2,4) P(x, y)

we have to find the points of P

x = (m1x2 + m2x1) / (m1 + m2)

m1 = 1, m2= 2

x1= 5, x2= 2

y1= 7, y2= 4

x= (1×2 + 2×5) / (1+2)

x= (2+10) / 3

x= 12/3

x= 4

y= (m1y2 + m2y1) / (m1 + m2)

y= (1×4 + 2×7) / (1+2)

y= (4+14)/3

y= 18/3

y= 6

Distance from origin = (4,6)