Question

Point T is the midpoint of RS, W is the midpoint of RT, and Z is the midpoint of WS. If the length of TZ is x, find the lengths of the following segments in terms of x.

A) RW B) WZ C) RS D)ZS

Answer 1

Let RS be y.

Given T is the midpoint of RS that is RT = TS =
`(y)/(2)`

And W is the midpoint of RT,

that is RW = WT =
`((y)/(2) )/(2) = (y)/(4)`

Given Z is the mid point of WS.

That is WZ = ZS =
`(WS)/(2) = (WT+TS)/(2) = (((y)/(4) +(y)/(2) ))/(2) =(3y)/(8)`

Now TZ = TS-ZS =
`(y)/(2) -(3y)/(8)  = (4y-3y)/(8) = (y)/(8)`

But TZ is given as x.

That is
`(y)/(8)  = x`

y=8x =RS.

A)length of RW =
`(y)/(4) = (8x)/(4) = 2x`

B) length of WZ =
`(3y)/(8) =(3*8x)/(8) = 3x`

C) length of RS = y =8x

D) length of ZS= WZ = 3x.

Image is attached for explanation.