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

Question

2 months ago

13

of the following segments in terms of x.
A) RW B) WZ C) RS D)ZS

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-03-24T10:16:04+03:00

Let RS be denoted as y.

Given that T is the midpoint of RS, this results in RT = TS = $\frac{y}{2}$

And W acting as the midpoint of RT, leads to

thus RW = WT = $\frac{\frac{y}{2} }{2} = \frac{y}{4}$

Given that Z is the midpoint of WS.

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

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

However, TZ is defined as x.

Thus, $\frac{y}{8} = x$

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.

An image is provided for clarification.