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 = $\frac{y}{2}$

And W is the midpoint of RT,

that is RW = WT = $\frac{\frac{y}{2} }{2} = \frac{y}{4}$

Given Z is the mid point of WS.

That is WZ = ZS = $\frac{WS}{2} = \frac{WT+TS}{2} = \frac{(\frac{y}{4} +\frac{y}{2} )}{2} =\frac{3y}{8}$

Now TZ = TS-ZS = $\frac{y}{2} -\frac{3y}{8} = \frac{4y-3y}{8} = \frac{y}{8}$

But TZ is given as x.

That is $\frac{y}{8} = x$

            y=8x =RS.

A)length of RW = $\frac{y}{4} = \frac{8x}{4} = 2x$

B) length of WZ = $\frac{3y}{8} =\frac{3*8x}{8} = 3x$

C) length of RS = y =8x

D) length of ZS= WZ = 3x.

Image is attached for explanation.