Question

if X, Y and Z divides the line segment PQ in four equal parts such that PX
= XY = YZ = ZQ , and the coordinates of P and Q are (1,6) and (3,-4)
respectively then find the coordinates of X, Y and Z.​

Answer 1

Answer:

Step-by-step explanation:

friend this is somewhat tricky question

as x y and z divides line segment into four equal parts

we can say y is mid point of pq

which is x1+x2/2,y1+y2/2

2,-1=y

and x is midpoint of p and y

which is x1+x2/2,y1+y2/2

3/2,-5/2=x

you find z by slope method

Mzq=Mpq

-4-y/3-x=5

-4-y=15-5x

5x-4y=15(equation 1)

Mzp=Mpq

y-6/x-1=5

y-6=5x-5

5x-y=-1(equation 2)

subtracting eq1 from eq 2

3y=-16

y=-16/3

and substitute it in eq 1

x=109/5

z=(109/5,-16/3)